{"id":189,"date":"2023-02-14T16:33:03","date_gmt":"2023-02-14T21:33:03","guid":{"rendered":"https:\/\/opentextbc.ca\/foundationsofphysics\/?post_type=chapter&#038;p=189"},"modified":"2023-09-12T14:43:42","modified_gmt":"2023-09-12T18:43:42","slug":"energy-heat","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/foundationsofphysics\/chapter\/energy-heat\/","title":{"raw":"Energy &amp; Heat","rendered":"Energy &amp; Heat"},"content":{"raw":"<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Resources<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ul>\r\n \t<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=eZdUKMDfJ_o\">Mechanical Universe - Episode 45 - Temperature and the Gas Law<\/a><\/li>\r\n \t<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=d6eJ8mccvu0\">Mechanical Universe - Episode 46 - The Engine of Nature<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"http:\/\/www.a-levelphysicstutor.com\/index-therm.php\">A-Level Physics Tutor<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\nEquations Introduced and Used for this Topic:\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\r\n \t<li>[latex]Q =\\pm mL_f[\/latex]<\/li>\r\n \t<li>[latex]Q =\\pm mL_v[\/latex]<\/li>\r\n<\/ul>\r\nWhere...\r\n<ul>\r\n \t<li>[latex]Q[\/latex] is the <strong>heat<\/strong> (energy), measured in joules (J)<\/li>\r\n \t<li>[latex]L_v[\/latex] is the <strong>latent heat of vaporization<\/strong>, measured in joules\/kilograms (J\/kg)<\/li>\r\n \t<li>[latex]L_f[\/latex] is the <strong>latent heat of fusion<\/strong>, measured in joules\/kilograms (J\/kg)<\/li>\r\n \t<li>[latex]\u2206T[\/latex] is the <strong>change in temperature<\/strong>, measured in Celsius (\u00b0C) or Kelvin (K)<\/li>\r\n \t<li>[latex]c[\/latex] is the<strong> specific heat constant<\/strong>, measured in joules\/kilograms degrees Celsius (J\/kg\u00b0C). Specific heat is found by experiment but has a rough value for specific temperature ranges.<\/li>\r\n \t<li>[latex]m[\/latex] is the <strong>mass<\/strong> of the object or substance being heated\/cooled, measured in kilograms (kg)<\/li>\r\n<\/ul>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Specific Heat<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Aluminum<\/th>\r\n<td style=\"width: 25%;\">900 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Lead<\/th>\r\n<td style=\"width: 25%;\">160 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Brass<\/th>\r\n<td style=\"width: 25%;\">384 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Mercury<\/th>\r\n<td style=\"width: 25%;\">139 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Copper<\/th>\r\n<td style=\"width: 25%;\">390 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Pyrex<\/th>\r\n<td style=\"width: 25%;\">837 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ethanol<\/th>\r\n<td style=\"width: 25%;\">2400 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Silver<\/th>\r\n<td style=\"width: 25%;\">235 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Glass<\/th>\r\n<td style=\"width: 25%;\">840 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steel<\/th>\r\n<td style=\"width: 25%;\">445 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ice<\/th>\r\n<td style=\"width: 25%;\">2100 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steam<\/th>\r\n<td style=\"width: 25%;\">2020 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Iron<\/th>\r\n<td style=\"width: 25%;\">460 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Water<\/th>\r\n<td style=\"width: 25%;\">4187 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Latent Heats of Fusion and Vaporization<\/caption>\r\n<tbody>\r\n<tr style=\"height: 18px;\">\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>f<\/sub> (J\/kg)<\/th>\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>v<\/sub> (J\/kg)<\/th>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Water<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">3.34 \u00d7 10<sup>5<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.26 \u00d7\u00a010<sup>6<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Mercury<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.18 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.96 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Ethyl Alcohol<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.05 \u00d7 10<sup>5<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">8.54\u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Nitrogen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.55 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.99 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Oxygen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.38 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.13 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Hydrogen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">5.86 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">4.52 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Helium<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">5.23 \u00d7 10<sup>3<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2 \u00d7 10<sup>4<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Fusion and Vaporization Temperatures<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>f<\/sub> (\u00b0C)<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>v<\/sub> (\u00b0C)<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Water<\/td>\r\n<td style=\"width: 33.3333%;\">0<\/td>\r\n<td style=\"width: 33.3333%;\">100<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Mercury<\/td>\r\n<td style=\"width: 33.3333%;\">\u221238.8<\/td>\r\n<td style=\"width: 33.3333%;\">356.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Aluminum<\/td>\r\n<td style=\"width: 33.3333%;\">660.3<\/td>\r\n<td style=\"width: 33.3333%;\">2519<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Nitrogen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212210<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212195.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Oxygen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212218.8<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212183<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Hydrogen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212259.1<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212252.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Helium<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212272.2<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212268.9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>15.1 Specific Heat Capacity<\/h1>\r\nEquations Introduced or Used for this Section:\r\n<p style=\"text-align: center;\">[latex]Q = mc\\Delta T[\/latex]<\/p>\r\n\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Specific Heat<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Aluminum<\/th>\r\n<td style=\"width: 25%;\">900 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Lead<\/th>\r\n<td style=\"width: 25%;\">160 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Brass<\/th>\r\n<td style=\"width: 25%;\">384 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Mercury<\/th>\r\n<td style=\"width: 25%;\">139 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Copper<\/th>\r\n<td style=\"width: 25%;\">390 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Pyrex<\/th>\r\n<td style=\"width: 25%;\">837 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ethanol<\/th>\r\n<td style=\"width: 25%;\">2400 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Silver<\/th>\r\n<td style=\"width: 25%;\">235 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Glass<\/th>\r\n<td style=\"width: 25%;\">840 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steel<\/th>\r\n<td style=\"width: 25%;\">445 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ice<\/th>\r\n<td style=\"width: 25%;\">2100 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steam<\/th>\r\n<td style=\"width: 25%;\">2020 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<tr>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Iron<\/th>\r\n<td style=\"width: 25%;\">460 J\/kg\u00b0C<\/td>\r\n<th style=\"width: 25%;\" scope=\"rowgroup\">Water<\/th>\r\n<td style=\"width: 25%;\">4187 J\/kg\u00b0C<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Heat and Temperature<\/h2>\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Introduction\">Introduction to Thermal Physics<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Introduction\">Temperature and Thermometers<\/a><\/li>\r\n \t<li>Extra Help:\u00a0<a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Thermometers-as-Speedometers\">Thermometers as Speedometers<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/What-is-Heat\">What is Heat<\/a><\/li>\r\n \t<li>Article to Read:\u00a0<a href=\"https:\/\/www.sciencealert.com\/finally-we-know-what-killed-sea-life-in-the-deadliest-mass-extinction-in-history?fbclid=IwAR36x4OmZVitcsiYt8Z9-KEB9VipXVI_NF6zruoNf08PK-HyhpHqompUNg4\">Finally, We Know What Killed Sea Life in The Deadliest Mass Extinction in History<\/a><\/li>\r\n \t<li>Article to Read: <a href=\"https:\/\/phys.org\/news\/2019-03-americans-thermostat-african-environmental-temperatures.html\">Researchers find Americans set their thermostat to match African environmental temperatures<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nSpecific Heat Capacity (Q) \u2013 or heat capacity \u2013 refers to the ability of a system or body\u2019s capability of absorbing or losing energy (heat energy) without changing its original state of solid, liquid, gas or plasma. What does occur in this setting is that the temperature of the object or system will change according to its gaining or losing heat energy.\r\n\r\nTemperature (T) refers to a measured value of a body using a thermometer that is calibrated in one or more scales such as Celsius (\u00b0C) or Kelvin (K) and in some cases Fahrenheit (\u00b0F). A common interpretation of temperature using the classical thermodynamics description is that it is measuring the average motion or the internal kinetic energies of the atoms or molecules making up a body or system. Temperature can also be thought of as the measurement of oscillation or vibrational motion that occurs in solids and liquids.\r\n\r\nEarly thermometers relied on the expansion of air or water as a way to measure the temperature of a body or a system. Examples of these thermometers can be seen at the Museo Galileo where the larger bulb at the bottom contains water to expand or contract and the thin tube shows this expansion using white dots representing 10 degree increments and single black dots showing single degree increments.\r\n\r\nThe beginning of precision temperature measurements is credited to Daniel Gabriel Fahrenheit (1686-1736) who based his scale on the lowest consistent temperature he could achieve in a lab by using a slurry of ice, water and salt (0\u00b0F), water and ice (32 \u00b0F) and the temperature of a human mouth or armpit (96\u00b0F). Fahrenheit deviated from the work of previous thermometer makers by using mercury as his choice of liquid to measure its expansion using heat energy.\r\n\r\nThe Celsius scale (centigrade scale) is the standard scale used in SI measurements. It is a variation of the original scale developed by Anders Celsius (1701-1744) who set the scale of 0\u00b0C as the boiling point of water and 100\u00b0C as the freezing point of water. Celsius\u2019s scale was reversed the next year to designating 0\u00b0C to represent the freezing point and 100\u00b0C to represent the boiling point. In 1954, the lowest possible temperature (Absolute Zero[footnote]In Fahrenheit, Absolute Zero is defined as \u2212459.67\u00b0F[\/footnote]) was defined to be exactly \u2212273.15\u00b0C.\r\n\r\nThe exact equivalent measure of temperature to Celsius is the measure of Kelvin (K) which starts at Absolute Zero as 0 K. Using this scale, the melting point of water is roughly 273.15 K and the boiling point is 373.15 K. Human temperature works out to be an average of 310.15 K.\r\n\r\nFor conversions:\r\n<p style=\"text-align: center;\">Kelvin = Celsius + 273.15\u00b0 and Fahrenheit = [latex]\\dfrac{5}{9}[\/latex] (Celsius \u2212 32\u00b0)<\/p>\r\n\r\n<h2>The Conceptual Development of Heat<\/h2>\r\nSome of the earliest conceptions of heat are from 3000 B.C., and can be found recorded in Egyptian hieroglyphs that relate heat to fire. While only fragments of the writings of Heraclitus (535 BCE-475 BCE) exist, recorded as quotes from other authors, his concept of heat (fire) was that it was responsible for controlling the nature of the other principle elements of earth and water. Al-Biruni (973-1050) related heat to the concept of movement and friction, where heat or cold related to motion of lack of motion by air. This concept of heat as related to motion was echoed and refined by a number of philosophers that followed: Abu Ali Sina (980-1037), Francis Bacon (1561-1626) and Robert Hooke (1635-1703).\r\n<div class=\"textbox textbox--sidebar\">Article to Read:\u00a0<a href=\"https:\/\/eic.rsc.org\/feature\/the-logic-of-phlogiston\/2000126.article\">The logic of Phlogiston<\/a><\/div>\r\nDominant in the historical development of the concept of heat was the phlogiston theory, which was later replaced by caloric theory. Phlogiston was considered to be an undetectable fluid-like substance that filled the spaces between matter. The properties of phlogiston, as needed to explain chemical and physical phenomenon, were in the end what scientists used to dismiss the fluid theory of heat.\r\n\r\nThe defining phenomenon used to dismiss phlogiston theory came from Sir Benjamin Thompson, a.k.a. Count Rumford[footnote]Benjamin Thompson (Count Rumford) has been quite entertaining for historians to research due to his military, political and amorous adventures.[\/footnote] (1753-1814), who found that it was the byproduct of mechanical energy from friction that produced heat and not some mysterious fluid that was being leaked from the substance. His breakthrough demonstration in 1804 was to immerse a cannon into a barrel of water and then use a dull drill bit to try to bore out the cannon. What happened is that the cold water in the barrel[footnote]Count Rumford recorded the amount of water in the barrel to be 2 1\u20444 wine gallons.[\/footnote] was brought to a boil within\u00a0 2 1\/2 hours, and no metal was removed from the barrel of the cannon, which meant that no phlogiston fluid from the cannon was escaping. Instead the amount of heat that was created was directly related to the amount of friction that was being produced.\r\n\r\nWithin a few decades, quantification experiments by James Joule (1818-1889), Robert Mayer (1814-1878) and others established a clear and measurable relationship between heat, mechanical energy and work. In 1847 Hermann Helmholtz (1821-1894) generalized the relationship between heat, mechanical energy and work into a universal law governing the conservation of energy. This came to be known as the First Law of Thermodynamics.\r\n\r\nThe <strong>First Law of Thermodynamics<\/strong> is a variation of the Law of Conservation of Energy that was adapted for Thermodynamic Systems[footnote]Reference - Thermodynamic System: https:\/\/en.wikipedia.org\/wiki\/Thermodynamic_system[\/footnote].\u00a0 It can be stated as follows: The total energy of an isolated system is constant where energy can be transformed from one form to another but energy can be neither created nor destroyed.\u00a0 In an equation this is written as:\r\n<p style=\"text-align: center;\">Internal Energy of a System = Heat added to a System \u2212 Work done by the System<\/p>\r\n<p style=\"text-align: center;\">or ... [latex]\\Delta U=Q\u2212W[\/latex]<\/p>\r\nThe year 1850 was a watershed in the history of science, marking the unification of the various and quite different studies of motion, light, heat, electricity, and magnetism under the umbrella of energy.\u00a0 Energy became the unifying concept that linked all of the above disparate fields of studies together and, as some historians argue, replaced the dominance of Astronomical studies with Physics.\r\n\r\nHeat is generally taught today as energy transferred between two systems or bodies due to a temperature difference or as a by-product of friction.\r\n<h2>Specific Heat Capacity<\/h2>\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>Extra Help: <a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/thermo\/spht.html\">Specific Heat<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"https:\/\/energyeducation.ca\/encyclopedia\/Heat_capacity\">Heat Capacity<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"https:\/\/energyeducation.ca\/encyclopedia\/Specific_heat_capacity\">Specific Heat Capacity<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nSpecific heat is the measure of the amount of heat energy needed to raise the temperature of a mass of one kilogram (kg) or gram (g) by one degree centigrade (1 \u00b0C) .\u00a0 This relationship allows one to quantify the amount of heat specific to substances.\r\n\r\nThis relationship is quantified as:\r\n<p style=\"text-align: center;\">[latex]Q = mc\\Delta T[\/latex]<\/p>\r\nThe constant \u201cc\u201d used in this equation is only an average constant for the substance, and generally falls as the temperature of the body decreases. Water is an unusual substance that has one of the highest heat capacity values of all substances. As such, it is incredibly important to moderating and maintaining stable climate environments on the planet and moderating the internal temperature of living organisms. All specific heats vary with temperature and composition.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n1.5 kg of Pyrex glass (specific heat 837 J\/kg\u00b0C) loses 2.51 \u00d7 10<sup>4<\/sup> J of heat.\u00a0 If the temperature of the glass is 80\u00b0C before cooling what is its final temperature?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = 2.51 \u00d7 10<sup>4<\/sup> J<\/li>\r\n \t<li>[latex]m[\/latex] = 1.5 kg<\/li>\r\n \t<li>[latex]c_{\\text{pyrex}}[\/latex] = 837 J\/kg\u00b0C<\/li>\r\n \t<li>[latex]T_i[\/latex] = 80\u00b0C<\/li>\r\n \t<li>[latex]T_f[\/latex] = Find<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\r\n \t<li>[latex]-2.51\\times10^4\\text{ J}=(1.5\\text{ kg})(837\\text{ J\/kg\u00b0C})(T_f-80\\text{\u00b0C})[\/latex]<\/li>\r\n \t<li>[latex]T_f-80\\text{\u00b0C}=-2.51\\times10^4\\text{ J}\\div 1256\\text{ J\/\u00b0C}[\/latex]<\/li>\r\n \t<li>[latex]T_f=60\\text{\u00b0C}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate the specific heat of a 286 kg piece of steel if 2.54 \u00d7 10<sup>7<\/sup> J of heat is required to raise its temperature from 20\u00b0C to 220\u00b0C.\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = 2.54 \u00d7 10<sup>7<\/sup> J<\/li>\r\n \t<li>[latex]m[\/latex] = 286 kg<\/li>\r\n \t<li>[latex]T_i[\/latex] = 20\u00b0C<\/li>\r\n \t<li>[latex]T_f[\/latex] = 220\u00b0C<\/li>\r\n \t<li>[latex]c_{\\text{steel}}[\/latex] = Find<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\r\n \t<li>[latex]2.54\\times10^7\\text{ J}=(286\\text{ kg})(c_{\\text{steel}})(220\\text{\u00b0C}-20\\text{\u00b0C})[\/latex]<\/li>\r\n \t<li>[latex]2.54\\times10^7\\text{ J}=(c_{\\text{steel}})(57200\\text{ kg\u00b0C})[\/latex]<\/li>\r\n \t<li>[latex]c_{\\text{steel}}=2.54\\times10^7\\text{ J}\\div 572000\\text{ kg\u00b0C}[\/latex]<\/li>\r\n \t<li>[latex]c_{\\text{steel}}=444\\text{ J\/kg\u00b0C}(\\approx440\\text{ J\/kg\u00b0C})[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.1.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy how much should the temperature of a 500 g mass of lead change if 6560 J of heat is added to it?\u00a0 (Specific heat of lead is 129 J\/kg\u00b0C).\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = 6560 J<\/li>\r\n \t<li>[latex]m[\/latex] = 0.500 kg<\/li>\r\n \t<li>[latex]c_{\\text{lead}}[\/latex] = 129 J\/kg\u00b0C<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\r\n \t<li>[latex]6560\\text{ J}=(0.500\\text{ kg})(129\\text{ J\/kg\u00b0C})(\\Delta T)[\/latex]<\/li>\r\n \t<li>[latex]6560\\text{ J}=(64.5\\text{ J\/kg\u00b0C})(\\Delta T)[\/latex]<\/li>\r\n \t<li>[latex]\\Delta T=6560\\text{ J}\\div 64.5\\text{ J\/kg\u00b0C}[\/latex]<\/li>\r\n \t<li>[latex]\\Delta T=120\\text{\u00b0C}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.1.4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA 450 g Pyrex beaker contains 185 g of water at 21.0\u00b0C. Given that the specific heat of Pyrex is 837 J\/kg\u00b0C, how much heat is needed to raise the temperature of this glass and water to 100\u00b0C?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = Find<\/li>\r\n \t<li>[latex]m_{\\text{water}}[\/latex] = 0.185 kg<\/li>\r\n \t<li>[latex]m_{\\text{pyrex}}[\/latex] = 0.450 kg<\/li>\r\n \t<li>[latex]T_i[\/latex] = 21.0\u00b0C<\/li>\r\n \t<li>[latex]T_f[\/latex] = 100\u00b0C<\/li>\r\n \t<li>[latex]c_{\\text{pyrex}}[\/latex] = 837 J\/kg\u00b0C<\/li>\r\n \t<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q = mc\\Delta T+mc\\Delta T[\/latex] (water + pyrex)<\/li>\r\n \t<li>[latex]Q=(0.450\\text{ kg})(837\\text{ J\/kg\u00b0C})(100\\text{\u00b0C}-21.0\\text{\u00b0C})+(0.185\\text{ kg})(4187\\text{ J\/kg\u00b0C})(100\\text{\u00b0C}-21.0\\text{\u00b0C})[\/latex]<\/li>\r\n \t<li>[latex]Q=29760\\text{ J}+61200\\text{ J}[\/latex]<\/li>\r\n \t<li>[latex]Q=90960\\text{ J}(\\approx91000\\text{ J}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 15.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>How much heat is required to raise the temperature of 153 kg of water from 15.0 \u00b0C to 35.0 \u00b0C?<\/li>\r\n \t<li>How much heat is lost if 865 g of aluminum (specific heat 900 J\/kg\u00b0C) is cooled from 120 \u00b0C to 55 \u00b0C ?<\/li>\r\n \t<li>585 kg of Pyrex glass (specific heat 837 J\/kg\u00b0C) loses 8.65 \u00d7 10<sup>6<\/sup> J of heat. If the temperature of the glass is 95.8 \u00b0C before cooling what is its final temperature?<\/li>\r\n \t<li>Calculate the specific heat of a 286 kg piece of steel if 5.53 \u00d7 10<sup>7<\/sup> J of heat is required to raise its temperature from 22 \u00b0C to 452 \u00b0C.<\/li>\r\n \t<li>By how much should the temperature of a 2.75 kg mass of lead change if 2.84 \u00d7 10<sup>4<\/sup> J of heat is added to it? (Specific heat of lead is 129 J\/kg\u00b0C).<\/li>\r\n \t<li>What is the maximum mass of water that can be brought from 15.0 \u00b0C to its boiling point if 2.93 \u00d7 10<sup>6<\/sup> J of heat is available?<\/li>\r\n \t<li>Calculate the specific heat of a 300 kg piece of a steel alloy, if 5.93 \u00d7 10<sup>7<\/sup> J is required to raise its temperature from 25 \u00b0C to 450\u00b0 C.<\/li>\r\n \t<li>A 215 g glass beaker contains 145 g of water at 18.5 \u00b0C. If the specific heat of glass is 840 J\/kg\u00b0C,\u00a0 how much heat is needed to raise the temperature of this glass and water to 98.5 \u00b0C?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>15.2 Heat &amp; Phase Changes<\/h1>\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>Article to Read:\u00a0<a href=\"https:\/\/www.space.com\/17217-big-bang-phase-change-theory.html\">Wolchover, N. (2012) Big Bang was Actually a Phase Change, New Theory Says<\/a><\/li>\r\n \t<li>Article to Read: <a href=\"https:\/\/www.livescience.com\/63999-fifth-form-of-matter-created.html\">Scientists Create Rare Fifth Form of Matter in Space for the First Time Ever<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\nEquations Introduced or Used for this Section:\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>[latex]Q =\\pm mL_f[\/latex]<\/li>\r\n \t<li>[latex]Q =\\pm mL_v[\/latex]<\/li>\r\n<\/ul>\r\nWhere...\r\n<ul>\r\n \t<li>[latex]Q[\/latex] is the <strong>heat<\/strong> (energy), measured in joules (J)<\/li>\r\n \t<li>[latex]L_v[\/latex] is the<strong> latent heat of vaporization<\/strong>, measured in joules\/kilogram (J\/kg)<\/li>\r\n \t<li>[latex]L_f[\/latex] is the <strong>latent heat of fusion<\/strong>, measured in joules\/kilogram (J\/kg)<\/li>\r\n \t<li>[latex]m[\/latex] is the <strong>mass<\/strong> of the object being heated or cooled, measured in kilograms (kg)<\/li>\r\n<\/ul>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Latent Heats of Fusion and Vaporization<\/caption>\r\n<tbody>\r\n<tr style=\"height: 18px;\">\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>f<\/sub> (J\/kg)<\/th>\r\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>v<\/sub> (J\/kg)<\/th>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Water<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">3.34 \u00d7 10<sup>5<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.26 \u00d7\u00a010<sup>6<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Mercury<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.18 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.96 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Ethyl Alcohol<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.05 \u00d7 10<sup>5<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">8.54\u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Nitrogen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.55 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.99 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Oxygen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">1.38 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2.13 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Hydrogen<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">5.86 \u00d7 10<sup>4<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">4.52 \u00d7 10<sup>5<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td>Helium<\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">5.23 \u00d7 10<sup>3<\/sup><\/td>\r\n<td style=\"width: 33.3333%; height: 18px;\">2 \u00d7 10<sup>4<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Fusion and Vaporization Temperatures<\/caption>\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">Material<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>f<\/sub> (\u00b0C)<\/th>\r\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>v<\/sub> (\u00b0C)<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Water<\/td>\r\n<td style=\"width: 33.3333%;\">0<\/td>\r\n<td style=\"width: 33.3333%;\">100<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Mercury<\/td>\r\n<td style=\"width: 33.3333%;\">\u221238.8<\/td>\r\n<td style=\"width: 33.3333%;\">356.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Aluminum<\/td>\r\n<td style=\"width: 33.3333%;\">660.3<\/td>\r\n<td style=\"width: 33.3333%;\">2519<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Nitrogen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212210<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212195.8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Oxygen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212218.8<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212183<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Hydrogen<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212259.1<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212252.9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">Helium<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212272.2<\/td>\r\n<td style=\"width: 33.3333%;\">\u2212268.9<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPhase changes are used to describe the change in state that occurs in a substance as it changes from a solid to a liquid to a gaseous state or sometimes to plasma. A feature of phase change is that bodies can change state without changing temperature. The earliest record of this observation dates back to 1761 when Joseph Black (1728-1799)[footnote]Black\u2019s discoveries arose from his work for producers of Scotch whisky in search of the ideal quantity of fuel and water for distillation purposes.[\/footnote] announced his discovery that ice absorbs heat without changing temperature in the process of melting. Black went on to show that different substances have different specific heats.\r\n\r\nWhile the enthalpy of systems defines four changes of state, only the phase change between solids &amp; liquids and liquids &amp; gases will be analyzed.\r\n\r\n<img class=\"aligncenter wp-image-871\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition.jpg\" alt=\"\" width=\"600\" height=\"592\" \/>\r\n\r\nAt the atomic level, what is visualized is in the transition between solid, liquid and gaseous states. In the sketch to the left the transition from (a) solid to liquid and the reverse is described as either freezing or melting. The equation used to quantify this transition is: [latex]Q =\\pm mL_f[\/latex] where the + or \u2212 sign refers to either the system absorbing energy to melt or losing energy to freeze.\r\n\r\nFor the transition from liquid to a gaseous state (b) the changes of states are described as vaporization or condensation. The equation quantifying this transition is: [latex]Q =\\pm mL_v[\/latex] where the + or \u2212 sign refers to either the system absorbing energy to vaporize or losing energy to condense. Neither equation makes any reference to temperature; if the positive sign is used, the system is absorbing energy and if the negative sign is used the system is losing energy.\r\n\r\nThe following examples work with the change in state of some substance.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nOn the following phase change diagram of water changing from ice to steam show the following: temperature for the phase changes, the positive\/negative signs for the phase changes that indicate the system is gaining or losing energy with the corresponding names of these changes.\r\n\r\n<img class=\"aligncenter wp-image-872 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1.png\" alt=\"\" width=\"2145\" height=\"2300\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nHow much heat is required to melt 100 kg of ice at 0 \u00b0C?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = find<\/li>\r\n \t<li>[latex]m[\/latex] = 100 kg<\/li>\r\n \t<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q=+mL_f[\/latex]<\/li>\r\n \t<li>[latex]Q[\/latex] = \u2212 (12 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\r\n \t<li>[latex]Q[\/latex] = \u2212 2.71 \u00d7 10<sup>7<\/sup> J (\u2248 \u2212 2.7 \u00d7 10<sup>7<\/sup> J)<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.2.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nHow much heat is released when 12 kg of steam at 100 \u00b0C is condensed to water at the same temperature?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = find<\/li>\r\n \t<li>[latex]m[\/latex] = 12 kg<\/li>\r\n \t<li>[latex]L_v[\/latex] = 2.26 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q = -mL_v[\/latex]<\/li>\r\n \t<li>[latex]Q[\/latex] = \u2212 (12 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\r\n \t<li>[latex]Q[\/latex] = \u22122.71\u00a0\u00d7 10<sup>7<\/sup> J (\u2248 \u22122.7 \u00d7 10<sup>7<\/sup> J)<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.2.4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nHow much heat is required to convert 250 g of ice at \u221210.0 \u00b0C to steam at 100 \u00b0C?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = Find<\/li>\r\n \t<li>[latex]m[\/latex] = 0.25 kg<\/li>\r\n \t<li>[latex]L_v[\/latex] = 2.26 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\r\n \t<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\r\n \t<li>[latex]c_{\\text{ice}}[\/latex]\u00a0= 2100 J\/kg\u00b0C<\/li>\r\n \t<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q=mc\\Delta T+mL_f+mc\\Delta T+mL_v[\/latex]<\/li>\r\n \t<li>[latex]Q[\/latex] = (0.250 kg)(2100 J\/kg\u00b0C)(0\u00b0C \u2212 \u221210\u00b0C) + (0.250 kg)(3.34 \u00d7 10<sup>5<\/sup> J\/kg) + (0.250 kg)(4187 J\/kg\u00b0C)(100\u00b0C \u2212 0\u00b0C) + (0.250 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\r\n \t<li>[latex]Q[\/latex] = 5250 J + 83<span style=\"margin-left: 0.25em;\">500<\/span> J + 104<span style=\"margin-left: 0.25em;\">000<\/span> J + 565<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\r\n \t<li>[latex]Q[\/latex] = 758<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 15.2.5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nHow much heat must be extracted to change 454 g of water at 20\u00b0C into ice at \u22126\u00b0C?\r\n\r\n<strong>Solution<\/strong>\r\n\r\nData:\r\n<ul>\r\n \t<li>[latex]Q[\/latex] = Find<\/li>\r\n \t<li>[latex]m[\/latex] = 0.454 kg<\/li>\r\n \t<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\r\n \t<li>[latex]c_{\\text{ice}}[\/latex] = 2100 J\/kg\u00b0C<\/li>\r\n \t<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\r\n<\/ul>\r\nSolution:\r\n<ul>\r\n \t<li>[latex]Q=mc\\Delta T-mL_f+mc\\Delta T[\/latex]<\/li>\r\n \t<li>[latex]Q[\/latex] = (0.454 kg)(2100 J\/kg\u00b0C)(\u22126\u00b0C \u2212 0\u00b0C) \u2212 (0.454 kg)(3.34 \u00d7 10<sup>5<\/sup> J\/kg) + (0.454 kg)(4187 J\/kg\u00b0C)(0\u00b0C \u2212 20\u00b0C)<\/li>\r\n \t<li>[latex]Q[\/latex] = \u22125720 J \u2212 151<span style=\"margin-left: 0.25em;\">600<\/span> J \u2212 38<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\r\n \t<li>[latex]Q[\/latex] = \u2212195<span style=\"margin-left: 0.25em;\">000<\/span> J (\u2248 \u2212200<span style=\"margin-left: 0.25em;\">000<\/span> J)<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 15.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>How much heat is required to melt 28.6 kg of ice at 0\u00b0C?<\/li>\r\n \t<li>How much heat is released when 423 g of steam at 100 \u00b0C is condensed to water at the same temperature?<\/li>\r\n \t<li>If 1.85 \u00d7 10<sup>4<\/sup> J of heat is released when 3.85 \u00d7 10<sup>\u22123<\/sup> kg of tungsten is condensed at its boiling point what is the latent heat of vaporization of tungsten?<\/li>\r\n \t<li>What mass of ethanol can be solidified by the removal of 9.53 \u00d7 10<sup>4<\/sup> J of heat at its melting point? The latent heat of fusion of ethanol is 1.05 \u00d7 10<sup>5<\/sup> J\/kg.<\/li>\r\n \t<li>How much heat is released when 454 g of steam at 100\u00b0C is condensed into water at the same temperature?<\/li>\r\n \t<li>A cooler is able to condense 12.0 kg of steam at 100\u00b0C into water at 100\u00b0C? in 2.0 h. Using this same cooler, what mass of water at 0\u00b0C should it be able to freeze into ice at 0\u00b0C in 2.0h?<\/li>\r\n \t<li>How much heat must be extracted from a litre of water at 50\u00b0C to turn it into ice at 0\u00b0C?<\/li>\r\n \t<li>How much heat is required to convert 1.15 kg of ice 0.00 \u00b0C to water at 21.5 \u00b0C ?<\/li>\r\n \t<li>How much heat is required to convert 86.3 g of ice at \u22125.0 \u00b0C to steam at 100 \u00b0C?<\/li>\r\n \t<li>How much heat must be extracted to change 500 g of water at 5.0\u00b0C into ice at \u22128.0\u00b0C?<\/li>\r\n \t<li>How much heat is required to change 4.0 kg of ice at 0\u00b0C to steam at 100\u00b0C?<\/li>\r\n \t<li>How much heat is need to melt the 2.5 \u00d7 10<sup>19<\/sup> kg of ice in Antarctica if we assume an ice temperature of \u221245 \u00b0C? How does this compare to all the energy of the Sun striking the Earth in one year?\u00a0 (Total solar energy incident on Earth is 5.4 \u00d7 10<sup>24<\/sup> J each year.)<\/li>\r\n \t<li>If the entire 2 850 000 km3 of Greenland[footnote]The mass of the Greenland ice sheet is approximately 2.62 \u00d7 10<sup>15<\/sup> kg.[\/footnote] ice sheet were to melt global sea levels would rise 7.2 m. If we are to assume that the average temperature of this ice is \u221225 \u00b0C, how much energy is needed to turn Greenland\u2019s ice cap into water at 0 \u00b0C?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 15.3.1: Heating Canada\u2019s Homes - An Exercise in the Geography of Energy<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA typical sized family home consumes about 1500 m<sup>3<\/sup> of natural gas a year to heat (19\u00b0C). This is equivalent to about 57 GJ of energy.\r\n<ol>\r\n \t<li>If we were to use wood with an energy density of 1.5 \u00d7 10<sup>7<\/sup> J\/kg, how many kg would we need to heat this house?<\/li>\r\n \t<li>If a hectare of forest provides 100<span style=\"margin-left: 0.25em;\">000<\/span> kg of wood, how much wood would be needed to heat all of Canada\u2019s 12 million or so homes?<\/li>\r\n \t<li>If we consider that a tree takes roughly 100 years to reach an optimal size for harvesting, what size of forest in Canada would we need to have sustainable heating?<\/li>\r\n \t<li>How does the sustainable forest needed for heating compare to Canada\u2019s forest and wooded areas of roughly 400 million hectares?<\/li>\r\n \t<li>How does this compare to BC\u2019s forest and wooded areas of 64 million hectares?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 15.3.2: Yearly Melt of Arctic Sea Ice<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-683\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902.png\" alt=\"\" width=\"600\" height=\"475\" \/>\r\n<ol>\r\n \t<li>If we assume an average thickness of 2.5 m for this ice being melted and that the ice is at a temperature of \u221250\u00b0C, how much energy is absorbed by this process in a year?<\/li>\r\n<\/ol>\r\nArctic melts around 8 000 000 km<sup>2<\/sup> (2.5 m thick) Heat needed = ______________\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Exercise Answers<\/h1>\r\n<h2>15.1 Specific Heat Capacity<\/h2>\r\n<ol class=\"twocolumn\">\r\n \t<li>1.28 \u00d7 10<sup>7<\/sup> J<\/li>\r\n \t<li>\u2212 50<span style=\"margin-left: 0.25em;\">600<\/span> J<\/li>\r\n \t<li>78.1 \u00b0C<\/li>\r\n \t<li>450 J\/kg\u00b0C<\/li>\r\n \t<li>79.4 \u00b0C<\/li>\r\n \t<li>8.25 kg<\/li>\r\n \t<li>465 J\/kg\u00b0C<\/li>\r\n \t<li>6.3 \u00d7 10<sup>4<\/sup> J<\/li>\r\n<\/ol>\r\n<h2>15.2 Heat &amp; Phase Changes<\/h2>\r\n<ol class=\"twocolumn\">\r\n \t<li>9.55 \u00d7 10<sup>6<\/sup> J<\/li>\r\n \t<li>9.56 \u00d7 10<sup>5<\/sup> J<\/li>\r\n \t<li>4.81 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\r\n \t<li>0.908 kg<\/li>\r\n \t<li>1.03 \u00d7 10<sup>6<\/sup> J<\/li>\r\n \t<li>81.2 kg<\/li>\r\n \t<li>\u2212 5.43 \u00d7 10<sup>5<\/sup> J<\/li>\r\n \t<li>4.87 \u00d7 10<sup>5<\/sup> J<\/li>\r\n \t<li>2.61 \u00d7 10<sup>5<\/sup> J<\/li>\r\n \t<li>\u2212 1.85 \u00d7 10<sup>5<\/sup> J<\/li>\r\n \t<li>1.21 \u00d7 10<sup>7<\/sup> J<\/li>\r\n \t<li>1.07 \u00d7 10<sup>25<\/sup> J<\/li>\r\n<\/ol>\r\n<h2>15.3.1 Heating Canada\u2019s Homes<\/h2>\r\n<ol>\r\n \t<li>3800 kg<\/li>\r\n \t<li>456<span style=\"margin-left: 0.25em;\">000<\/span> ha\/y<\/li>\r\n \t<li>45.6 million hectares<\/li>\r\n \t<li>[latex]\\dfrac{57}{500}[\/latex] or 11.4%<\/li>\r\n \t<li>[latex]\\dfrac{57}{80}[\/latex] or 71%<\/li>\r\n<\/ol>\r\n<h2>15.3.2 Yearly Melt of Arctic Sea Ice<\/h2>\r\n<ol>\r\n \t<li>8 \u00d7 10<sup>21<\/sup>\u00a0J<\/li>\r\n<\/ol>\r\n<h3>Media Attributions<\/h3>\r\n<ul>\r\n \t<li>\"Energy transition sketch\" from <a href=\"https:\/\/openstax.org\/details\/books\/college-physics\">College Physics<\/a> by Openstax is licensed under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 licence<\/a>.<\/li>\r\n \t<li>\"<a href=\"https:\/\/nsidc.org\/arcticseaicenews\/2010\/01\/\">Arctic Sea Ice Extent January 2010<\/a>\" courtesy of the <a href=\"https:\/\/nsidc.org\/about\/data-use-and-copyright\">National Snow and Ice Data Center<\/a>, University of Colorado, Boulder.<\/li>\r\n<\/ul>","rendered":"<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Resources<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=eZdUKMDfJ_o\">Mechanical Universe &#8211; Episode 45 &#8211; Temperature and the Gas Law<\/a><\/li>\n<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=d6eJ8mccvu0\">Mechanical Universe &#8211; Episode 46 &#8211; The Engine of Nature<\/a><\/li>\n<li>Extra Help: <a href=\"http:\/\/www.a-levelphysicstutor.com\/index-therm.php\">A-Level Physics Tutor<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>Equations Introduced and Used for this Topic:<\/p>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\n<li>[latex]Q =\\pm mL_f[\/latex]<\/li>\n<li>[latex]Q =\\pm mL_v[\/latex]<\/li>\n<\/ul>\n<p>Where&#8230;<\/p>\n<ul>\n<li>[latex]Q[\/latex] is the <strong>heat<\/strong> (energy), measured in joules (J)<\/li>\n<li>[latex]L_v[\/latex] is the <strong>latent heat of vaporization<\/strong>, measured in joules\/kilograms (J\/kg)<\/li>\n<li>[latex]L_f[\/latex] is the <strong>latent heat of fusion<\/strong>, measured in joules\/kilograms (J\/kg)<\/li>\n<li>[latex]\u2206T[\/latex] is the <strong>change in temperature<\/strong>, measured in Celsius (\u00b0C) or Kelvin (K)<\/li>\n<li>[latex]c[\/latex] is the<strong> specific heat constant<\/strong>, measured in joules\/kilograms degrees Celsius (J\/kg\u00b0C). Specific heat is found by experiment but has a rough value for specific temperature ranges.<\/li>\n<li>[latex]m[\/latex] is the <strong>mass<\/strong> of the object or substance being heated\/cooled, measured in kilograms (kg)<\/li>\n<\/ul>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Specific Heat<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Aluminum<\/th>\n<td style=\"width: 25%;\">900 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Lead<\/th>\n<td style=\"width: 25%;\">160 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Brass<\/th>\n<td style=\"width: 25%;\">384 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Mercury<\/th>\n<td style=\"width: 25%;\">139 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Copper<\/th>\n<td style=\"width: 25%;\">390 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Pyrex<\/th>\n<td style=\"width: 25%;\">837 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ethanol<\/th>\n<td style=\"width: 25%;\">2400 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Silver<\/th>\n<td style=\"width: 25%;\">235 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Glass<\/th>\n<td style=\"width: 25%;\">840 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steel<\/th>\n<td style=\"width: 25%;\">445 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ice<\/th>\n<td style=\"width: 25%;\">2100 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steam<\/th>\n<td style=\"width: 25%;\">2020 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Iron<\/th>\n<td style=\"width: 25%;\">460 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Water<\/th>\n<td style=\"width: 25%;\">4187 J\/kg\u00b0C<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Latent Heats of Fusion and Vaporization<\/caption>\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">Material<\/th>\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>f<\/sub> (J\/kg)<\/th>\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>v<\/sub> (J\/kg)<\/th>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Water<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">3.34 \u00d7 10<sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.26 \u00d7\u00a010<sup>6<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Mercury<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.18 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.96 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Ethyl Alcohol<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.05 \u00d7 10<sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">8.54\u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Nitrogen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.55 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.99 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Oxygen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.38 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.13 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Hydrogen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">5.86 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">4.52 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Helium<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">5.23 \u00d7 10<sup>3<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2 \u00d7 10<sup>4<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Fusion and Vaporization Temperatures<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 33.3333%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>f<\/sub> (\u00b0C)<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>v<\/sub> (\u00b0C)<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Water<\/td>\n<td style=\"width: 33.3333%;\">0<\/td>\n<td style=\"width: 33.3333%;\">100<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Mercury<\/td>\n<td style=\"width: 33.3333%;\">\u221238.8<\/td>\n<td style=\"width: 33.3333%;\">356.7<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Aluminum<\/td>\n<td style=\"width: 33.3333%;\">660.3<\/td>\n<td style=\"width: 33.3333%;\">2519<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Nitrogen<\/td>\n<td style=\"width: 33.3333%;\">\u2212210<\/td>\n<td style=\"width: 33.3333%;\">\u2212195.8<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Oxygen<\/td>\n<td style=\"width: 33.3333%;\">\u2212218.8<\/td>\n<td style=\"width: 33.3333%;\">\u2212183<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Hydrogen<\/td>\n<td style=\"width: 33.3333%;\">\u2212259.1<\/td>\n<td style=\"width: 33.3333%;\">\u2212252.9<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Helium<\/td>\n<td style=\"width: 33.3333%;\">\u2212272.2<\/td>\n<td style=\"width: 33.3333%;\">\u2212268.9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>15.1 Specific Heat Capacity<\/h1>\n<p>Equations Introduced or Used for this Section:<\/p>\n<p style=\"text-align: center;\">[latex]Q = mc\\Delta T[\/latex]<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Specific Heat<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 25%;\" scope=\"col\">Specific Heat<\/th>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Aluminum<\/th>\n<td style=\"width: 25%;\">900 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Lead<\/th>\n<td style=\"width: 25%;\">160 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Brass<\/th>\n<td style=\"width: 25%;\">384 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Mercury<\/th>\n<td style=\"width: 25%;\">139 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Copper<\/th>\n<td style=\"width: 25%;\">390 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Pyrex<\/th>\n<td style=\"width: 25%;\">837 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ethanol<\/th>\n<td style=\"width: 25%;\">2400 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Silver<\/th>\n<td style=\"width: 25%;\">235 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Glass<\/th>\n<td style=\"width: 25%;\">840 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steel<\/th>\n<td style=\"width: 25%;\">445 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Ice<\/th>\n<td style=\"width: 25%;\">2100 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Steam<\/th>\n<td style=\"width: 25%;\">2020 J\/kg\u00b0C<\/td>\n<\/tr>\n<tr>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Iron<\/th>\n<td style=\"width: 25%;\">460 J\/kg\u00b0C<\/td>\n<th style=\"width: 25%;\" scope=\"rowgroup\">Water<\/th>\n<td style=\"width: 25%;\">4187 J\/kg\u00b0C<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Heat and Temperature<\/h2>\n<div class=\"textbox\">\n<ul>\n<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Introduction\">Introduction to Thermal Physics<\/a><\/li>\n<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Introduction\">Temperature and Thermometers<\/a><\/li>\n<li>Extra Help:\u00a0<a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/Thermometers-as-Speedometers\">Thermometers as Speedometers<\/a><\/li>\n<li>Extra Help: <a href=\"https:\/\/www.physicsclassroom.com\/class\/thermalP\/Lesson-1\/What-is-Heat\">What is Heat<\/a><\/li>\n<li>Article to Read:\u00a0<a href=\"https:\/\/www.sciencealert.com\/finally-we-know-what-killed-sea-life-in-the-deadliest-mass-extinction-in-history?fbclid=IwAR36x4OmZVitcsiYt8Z9-KEB9VipXVI_NF6zruoNf08PK-HyhpHqompUNg4\">Finally, We Know What Killed Sea Life in The Deadliest Mass Extinction in History<\/a><\/li>\n<li>Article to Read: <a href=\"https:\/\/phys.org\/news\/2019-03-americans-thermostat-african-environmental-temperatures.html\">Researchers find Americans set their thermostat to match African environmental temperatures<\/a><\/li>\n<\/ul>\n<\/div>\n<p>Specific Heat Capacity (Q) \u2013 or heat capacity \u2013 refers to the ability of a system or body\u2019s capability of absorbing or losing energy (heat energy) without changing its original state of solid, liquid, gas or plasma. What does occur in this setting is that the temperature of the object or system will change according to its gaining or losing heat energy.<\/p>\n<p>Temperature (T) refers to a measured value of a body using a thermometer that is calibrated in one or more scales such as Celsius (\u00b0C) or Kelvin (K) and in some cases Fahrenheit (\u00b0F). A common interpretation of temperature using the classical thermodynamics description is that it is measuring the average motion or the internal kinetic energies of the atoms or molecules making up a body or system. Temperature can also be thought of as the measurement of oscillation or vibrational motion that occurs in solids and liquids.<\/p>\n<p>Early thermometers relied on the expansion of air or water as a way to measure the temperature of a body or a system. Examples of these thermometers can be seen at the Museo Galileo where the larger bulb at the bottom contains water to expand or contract and the thin tube shows this expansion using white dots representing 10 degree increments and single black dots showing single degree increments.<\/p>\n<p>The beginning of precision temperature measurements is credited to Daniel Gabriel Fahrenheit (1686-1736) who based his scale on the lowest consistent temperature he could achieve in a lab by using a slurry of ice, water and salt (0\u00b0F), water and ice (32 \u00b0F) and the temperature of a human mouth or armpit (96\u00b0F). Fahrenheit deviated from the work of previous thermometer makers by using mercury as his choice of liquid to measure its expansion using heat energy.<\/p>\n<p>The Celsius scale (centigrade scale) is the standard scale used in SI measurements. It is a variation of the original scale developed by Anders Celsius (1701-1744) who set the scale of 0\u00b0C as the boiling point of water and 100\u00b0C as the freezing point of water. Celsius\u2019s scale was reversed the next year to designating 0\u00b0C to represent the freezing point and 100\u00b0C to represent the boiling point. In 1954, the lowest possible temperature (Absolute Zero<a class=\"footnote\" title=\"In Fahrenheit, Absolute Zero is defined as \u2212459.67\u00b0F\" id=\"return-footnote-189-1\" href=\"#footnote-189-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>) was defined to be exactly \u2212273.15\u00b0C.<\/p>\n<p>The exact equivalent measure of temperature to Celsius is the measure of Kelvin (K) which starts at Absolute Zero as 0 K. Using this scale, the melting point of water is roughly 273.15 K and the boiling point is 373.15 K. Human temperature works out to be an average of 310.15 K.<\/p>\n<p>For conversions:<\/p>\n<p style=\"text-align: center;\">Kelvin = Celsius + 273.15\u00b0 and Fahrenheit = [latex]\\dfrac{5}{9}[\/latex] (Celsius \u2212 32\u00b0)<\/p>\n<h2>The Conceptual Development of Heat<\/h2>\n<p>Some of the earliest conceptions of heat are from 3000 B.C., and can be found recorded in Egyptian hieroglyphs that relate heat to fire. While only fragments of the writings of Heraclitus (535 BCE-475 BCE) exist, recorded as quotes from other authors, his concept of heat (fire) was that it was responsible for controlling the nature of the other principle elements of earth and water. Al-Biruni (973-1050) related heat to the concept of movement and friction, where heat or cold related to motion of lack of motion by air. This concept of heat as related to motion was echoed and refined by a number of philosophers that followed: Abu Ali Sina (980-1037), Francis Bacon (1561-1626) and Robert Hooke (1635-1703).<\/p>\n<div class=\"textbox textbox--sidebar\">Article to Read:\u00a0<a href=\"https:\/\/eic.rsc.org\/feature\/the-logic-of-phlogiston\/2000126.article\">The logic of Phlogiston<\/a><\/div>\n<p>Dominant in the historical development of the concept of heat was the phlogiston theory, which was later replaced by caloric theory. Phlogiston was considered to be an undetectable fluid-like substance that filled the spaces between matter. The properties of phlogiston, as needed to explain chemical and physical phenomenon, were in the end what scientists used to dismiss the fluid theory of heat.<\/p>\n<p>The defining phenomenon used to dismiss phlogiston theory came from Sir Benjamin Thompson, a.k.a. Count Rumford<a class=\"footnote\" title=\"Benjamin Thompson (Count Rumford) has been quite entertaining for historians to research due to his military, political and amorous adventures.\" id=\"return-footnote-189-2\" href=\"#footnote-189-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> (1753-1814), who found that it was the byproduct of mechanical energy from friction that produced heat and not some mysterious fluid that was being leaked from the substance. His breakthrough demonstration in 1804 was to immerse a cannon into a barrel of water and then use a dull drill bit to try to bore out the cannon. What happened is that the cold water in the barrel<a class=\"footnote\" title=\"Count Rumford recorded the amount of water in the barrel to be 2 1\u20444 wine gallons.\" id=\"return-footnote-189-3\" href=\"#footnote-189-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a> was brought to a boil within\u00a0 2 1\/2 hours, and no metal was removed from the barrel of the cannon, which meant that no phlogiston fluid from the cannon was escaping. Instead the amount of heat that was created was directly related to the amount of friction that was being produced.<\/p>\n<p>Within a few decades, quantification experiments by James Joule (1818-1889), Robert Mayer (1814-1878) and others established a clear and measurable relationship between heat, mechanical energy and work. In 1847 Hermann Helmholtz (1821-1894) generalized the relationship between heat, mechanical energy and work into a universal law governing the conservation of energy. This came to be known as the First Law of Thermodynamics.<\/p>\n<p>The <strong>First Law of Thermodynamics<\/strong> is a variation of the Law of Conservation of Energy that was adapted for Thermodynamic Systems<a class=\"footnote\" title=\"Reference - Thermodynamic System: https:\/\/en.wikipedia.org\/wiki\/Thermodynamic_system\" id=\"return-footnote-189-4\" href=\"#footnote-189-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a>.\u00a0 It can be stated as follows: The total energy of an isolated system is constant where energy can be transformed from one form to another but energy can be neither created nor destroyed.\u00a0 In an equation this is written as:<\/p>\n<p style=\"text-align: center;\">Internal Energy of a System = Heat added to a System \u2212 Work done by the System<\/p>\n<p style=\"text-align: center;\">or &#8230; [latex]\\Delta U=Q\u2212W[\/latex]<\/p>\n<p>The year 1850 was a watershed in the history of science, marking the unification of the various and quite different studies of motion, light, heat, electricity, and magnetism under the umbrella of energy.\u00a0 Energy became the unifying concept that linked all of the above disparate fields of studies together and, as some historians argue, replaced the dominance of Astronomical studies with Physics.<\/p>\n<p>Heat is generally taught today as energy transferred between two systems or bodies due to a temperature difference or as a by-product of friction.<\/p>\n<h2>Specific Heat Capacity<\/h2>\n<div class=\"textbox\">\n<ul>\n<li>Extra Help: <a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/thermo\/spht.html\">Specific Heat<\/a><\/li>\n<li>Extra Help: <a href=\"https:\/\/energyeducation.ca\/encyclopedia\/Heat_capacity\">Heat Capacity<\/a><\/li>\n<li>Extra Help: <a href=\"https:\/\/energyeducation.ca\/encyclopedia\/Specific_heat_capacity\">Specific Heat Capacity<\/a><\/li>\n<\/ul>\n<\/div>\n<p>Specific heat is the measure of the amount of heat energy needed to raise the temperature of a mass of one kilogram (kg) or gram (g) by one degree centigrade (1 \u00b0C) .\u00a0 This relationship allows one to quantify the amount of heat specific to substances.<\/p>\n<p>This relationship is quantified as:<\/p>\n<p style=\"text-align: center;\">[latex]Q = mc\\Delta T[\/latex]<\/p>\n<p>The constant \u201cc\u201d used in this equation is only an average constant for the substance, and generally falls as the temperature of the body decreases. Water is an unusual substance that has one of the highest heat capacity values of all substances. As such, it is incredibly important to moderating and maintaining stable climate environments on the planet and moderating the internal temperature of living organisms. All specific heats vary with temperature and composition.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>1.5 kg of Pyrex glass (specific heat 837 J\/kg\u00b0C) loses 2.51 \u00d7 10<sup>4<\/sup> J of heat.\u00a0 If the temperature of the glass is 80\u00b0C before cooling what is its final temperature?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = 2.51 \u00d7 10<sup>4<\/sup> J<\/li>\n<li>[latex]m[\/latex] = 1.5 kg<\/li>\n<li>[latex]c_{\\text{pyrex}}[\/latex] = 837 J\/kg\u00b0C<\/li>\n<li>[latex]T_i[\/latex] = 80\u00b0C<\/li>\n<li>[latex]T_f[\/latex] = Find<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\n<li>[latex]-2.51\\times10^4\\text{ J}=(1.5\\text{ kg})(837\\text{ J\/kg\u00b0C})(T_f-80\\text{\u00b0C})[\/latex]<\/li>\n<li>[latex]T_f-80\\text{\u00b0C}=-2.51\\times10^4\\text{ J}\\div 1256\\text{ J\/\u00b0C}[\/latex]<\/li>\n<li>[latex]T_f=60\\text{\u00b0C}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the specific heat of a 286 kg piece of steel if 2.54 \u00d7 10<sup>7<\/sup> J of heat is required to raise its temperature from 20\u00b0C to 220\u00b0C.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = 2.54 \u00d7 10<sup>7<\/sup> J<\/li>\n<li>[latex]m[\/latex] = 286 kg<\/li>\n<li>[latex]T_i[\/latex] = 20\u00b0C<\/li>\n<li>[latex]T_f[\/latex] = 220\u00b0C<\/li>\n<li>[latex]c_{\\text{steel}}[\/latex] = Find<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\n<li>[latex]2.54\\times10^7\\text{ J}=(286\\text{ kg})(c_{\\text{steel}})(220\\text{\u00b0C}-20\\text{\u00b0C})[\/latex]<\/li>\n<li>[latex]2.54\\times10^7\\text{ J}=(c_{\\text{steel}})(57200\\text{ kg\u00b0C})[\/latex]<\/li>\n<li>[latex]c_{\\text{steel}}=2.54\\times10^7\\text{ J}\\div 572000\\text{ kg\u00b0C}[\/latex]<\/li>\n<li>[latex]c_{\\text{steel}}=444\\text{ J\/kg\u00b0C}(\\approx440\\text{ J\/kg\u00b0C})[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.1.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By how much should the temperature of a 500 g mass of lead change if 6560 J of heat is added to it?\u00a0 (Specific heat of lead is 129 J\/kg\u00b0C).<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = 6560 J<\/li>\n<li>[latex]m[\/latex] = 0.500 kg<\/li>\n<li>[latex]c_{\\text{lead}}[\/latex] = 129 J\/kg\u00b0C<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q = mc\\Delta T[\/latex]<\/li>\n<li>[latex]6560\\text{ J}=(0.500\\text{ kg})(129\\text{ J\/kg\u00b0C})(\\Delta T)[\/latex]<\/li>\n<li>[latex]6560\\text{ J}=(64.5\\text{ J\/kg\u00b0C})(\\Delta T)[\/latex]<\/li>\n<li>[latex]\\Delta T=6560\\text{ J}\\div 64.5\\text{ J\/kg\u00b0C}[\/latex]<\/li>\n<li>[latex]\\Delta T=120\\text{\u00b0C}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.1.4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A 450 g Pyrex beaker contains 185 g of water at 21.0\u00b0C. Given that the specific heat of Pyrex is 837 J\/kg\u00b0C, how much heat is needed to raise the temperature of this glass and water to 100\u00b0C?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = Find<\/li>\n<li>[latex]m_{\\text{water}}[\/latex] = 0.185 kg<\/li>\n<li>[latex]m_{\\text{pyrex}}[\/latex] = 0.450 kg<\/li>\n<li>[latex]T_i[\/latex] = 21.0\u00b0C<\/li>\n<li>[latex]T_f[\/latex] = 100\u00b0C<\/li>\n<li>[latex]c_{\\text{pyrex}}[\/latex] = 837 J\/kg\u00b0C<\/li>\n<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q = mc\\Delta T+mc\\Delta T[\/latex] (water + pyrex)<\/li>\n<li>[latex]Q=(0.450\\text{ kg})(837\\text{ J\/kg\u00b0C})(100\\text{\u00b0C}-21.0\\text{\u00b0C})+(0.185\\text{ kg})(4187\\text{ J\/kg\u00b0C})(100\\text{\u00b0C}-21.0\\text{\u00b0C})[\/latex]<\/li>\n<li>[latex]Q=29760\\text{ J}+61200\\text{ J}[\/latex]<\/li>\n<li>[latex]Q=90960\\text{ J}(\\approx91000\\text{ J}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>How much heat is required to raise the temperature of 153 kg of water from 15.0 \u00b0C to 35.0 \u00b0C?<\/li>\n<li>How much heat is lost if 865 g of aluminum (specific heat 900 J\/kg\u00b0C) is cooled from 120 \u00b0C to 55 \u00b0C ?<\/li>\n<li>585 kg of Pyrex glass (specific heat 837 J\/kg\u00b0C) loses 8.65 \u00d7 10<sup>6<\/sup> J of heat. If the temperature of the glass is 95.8 \u00b0C before cooling what is its final temperature?<\/li>\n<li>Calculate the specific heat of a 286 kg piece of steel if 5.53 \u00d7 10<sup>7<\/sup> J of heat is required to raise its temperature from 22 \u00b0C to 452 \u00b0C.<\/li>\n<li>By how much should the temperature of a 2.75 kg mass of lead change if 2.84 \u00d7 10<sup>4<\/sup> J of heat is added to it? (Specific heat of lead is 129 J\/kg\u00b0C).<\/li>\n<li>What is the maximum mass of water that can be brought from 15.0 \u00b0C to its boiling point if 2.93 \u00d7 10<sup>6<\/sup> J of heat is available?<\/li>\n<li>Calculate the specific heat of a 300 kg piece of a steel alloy, if 5.93 \u00d7 10<sup>7<\/sup> J is required to raise its temperature from 25 \u00b0C to 450\u00b0 C.<\/li>\n<li>A 215 g glass beaker contains 145 g of water at 18.5 \u00b0C. If the specific heat of glass is 840 J\/kg\u00b0C,\u00a0 how much heat is needed to raise the temperature of this glass and water to 98.5 \u00b0C?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>15.2 Heat &amp; Phase Changes<\/h1>\n<div class=\"textbox\">\n<ul>\n<li>Article to Read:\u00a0<a href=\"https:\/\/www.space.com\/17217-big-bang-phase-change-theory.html\">Wolchover, N. (2012) Big Bang was Actually a Phase Change, New Theory Says<\/a><\/li>\n<li>Article to Read: <a href=\"https:\/\/www.livescience.com\/63999-fifth-form-of-matter-created.html\">Scientists Create Rare Fifth Form of Matter in Space for the First Time Ever<\/a><\/li>\n<\/ul>\n<\/div>\n<p>Equations Introduced or Used for this Section:<\/p>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>[latex]Q =\\pm mL_f[\/latex]<\/li>\n<li>[latex]Q =\\pm mL_v[\/latex]<\/li>\n<\/ul>\n<p>Where&#8230;<\/p>\n<ul>\n<li>[latex]Q[\/latex] is the <strong>heat<\/strong> (energy), measured in joules (J)<\/li>\n<li>[latex]L_v[\/latex] is the<strong> latent heat of vaporization<\/strong>, measured in joules\/kilogram (J\/kg)<\/li>\n<li>[latex]L_f[\/latex] is the <strong>latent heat of fusion<\/strong>, measured in joules\/kilogram (J\/kg)<\/li>\n<li>[latex]m[\/latex] is the <strong>mass<\/strong> of the object being heated or cooled, measured in kilograms (kg)<\/li>\n<\/ul>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Latent Heats of Fusion and Vaporization<\/caption>\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">Material<\/th>\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>f<\/sub> (J\/kg)<\/th>\n<th style=\"width: 33.3333%; height: 18px;\" scope=\"col\">L<sub>v<\/sub> (J\/kg)<\/th>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Water<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">3.34 \u00d7 10<sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.26 \u00d7\u00a010<sup>6<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Mercury<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.18 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.96 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Ethyl Alcohol<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.05 \u00d7 10<sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">8.54\u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Nitrogen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.55 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.99 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Oxygen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">1.38 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2.13 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Hydrogen<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">5.86 \u00d7 10<sup>4<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">4.52 \u00d7 10<sup>5<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td>Helium<\/td>\n<td style=\"width: 33.3333%; height: 18px;\">5.23 \u00d7 10<sup>3<\/sup><\/td>\n<td style=\"width: 33.3333%; height: 18px;\">2 \u00d7 10<sup>4<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<caption>Fusion and Vaporization Temperatures<\/caption>\n<tbody>\n<tr>\n<th style=\"width: 33.3333%;\" scope=\"col\">Material<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>f<\/sub> (\u00b0C)<\/th>\n<th style=\"width: 33.3333%;\" scope=\"col\">T<sub>v<\/sub> (\u00b0C)<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Water<\/td>\n<td style=\"width: 33.3333%;\">0<\/td>\n<td style=\"width: 33.3333%;\">100<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Mercury<\/td>\n<td style=\"width: 33.3333%;\">\u221238.8<\/td>\n<td style=\"width: 33.3333%;\">356.7<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Aluminum<\/td>\n<td style=\"width: 33.3333%;\">660.3<\/td>\n<td style=\"width: 33.3333%;\">2519<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Nitrogen<\/td>\n<td style=\"width: 33.3333%;\">\u2212210<\/td>\n<td style=\"width: 33.3333%;\">\u2212195.8<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Oxygen<\/td>\n<td style=\"width: 33.3333%;\">\u2212218.8<\/td>\n<td style=\"width: 33.3333%;\">\u2212183<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Hydrogen<\/td>\n<td style=\"width: 33.3333%;\">\u2212259.1<\/td>\n<td style=\"width: 33.3333%;\">\u2212252.9<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">Helium<\/td>\n<td style=\"width: 33.3333%;\">\u2212272.2<\/td>\n<td style=\"width: 33.3333%;\">\u2212268.9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Phase changes are used to describe the change in state that occurs in a substance as it changes from a solid to a liquid to a gaseous state or sometimes to plasma. A feature of phase change is that bodies can change state without changing temperature. The earliest record of this observation dates back to 1761 when Joseph Black (1728-1799)<a class=\"footnote\" title=\"Black\u2019s discoveries arose from his work for producers of Scotch whisky in search of the ideal quantity of fuel and water for distillation purposes.\" id=\"return-footnote-189-5\" href=\"#footnote-189-5\" aria-label=\"Footnote 5\"><sup class=\"footnote\">[5]<\/sup><\/a> announced his discovery that ice absorbs heat without changing temperature in the process of melting. Black went on to show that different substances have different specific heats.<\/p>\n<p>While the enthalpy of systems defines four changes of state, only the phase change between solids &amp; liquids and liquids &amp; gases will be analyzed.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-871\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition.jpg\" alt=\"\" width=\"600\" height=\"592\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition.jpg 875w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition-300x296.jpg 300w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition-768x758.jpg 768w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition-65x64.jpg 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition-225x222.jpg 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/heat-transition-350x346.jpg 350w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>At the atomic level, what is visualized is in the transition between solid, liquid and gaseous states. In the sketch to the left the transition from (a) solid to liquid and the reverse is described as either freezing or melting. The equation used to quantify this transition is: [latex]Q =\\pm mL_f[\/latex] where the + or \u2212 sign refers to either the system absorbing energy to melt or losing energy to freeze.<\/p>\n<p>For the transition from liquid to a gaseous state (b) the changes of states are described as vaporization or condensation. The equation quantifying this transition is: [latex]Q =\\pm mL_v[\/latex] where the + or \u2212 sign refers to either the system absorbing energy to vaporize or losing energy to condense. Neither equation makes any reference to temperature; if the positive sign is used, the system is absorbing energy and if the negative sign is used the system is losing energy.<\/p>\n<p>The following examples work with the change in state of some substance.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>On the following phase change diagram of water changing from ice to steam show the following: temperature for the phase changes, the positive\/negative signs for the phase changes that indicate the system is gaining or losing energy with the corresponding names of these changes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-872 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1.png\" alt=\"\" width=\"2145\" height=\"2300\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1.png 2145w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-280x300.png 280w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-955x1024.png 955w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-768x823.png 768w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-1432x1536.png 1432w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-1910x2048.png 1910w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-65x70.png 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-225x241.png 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/15.2.1-350x375.png 350w\" sizes=\"auto, (max-width: 2145px) 100vw, 2145px\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>How much heat is required to melt 100 kg of ice at 0 \u00b0C?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = find<\/li>\n<li>[latex]m[\/latex] = 100 kg<\/li>\n<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q=+mL_f[\/latex]<\/li>\n<li>[latex]Q[\/latex] = \u2212 (12 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\n<li>[latex]Q[\/latex] = \u2212 2.71 \u00d7 10<sup>7<\/sup> J (\u2248 \u2212 2.7 \u00d7 10<sup>7<\/sup> J)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.2.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>How much heat is released when 12 kg of steam at 100 \u00b0C is condensed to water at the same temperature?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = find<\/li>\n<li>[latex]m[\/latex] = 12 kg<\/li>\n<li>[latex]L_v[\/latex] = 2.26 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q = -mL_v[\/latex]<\/li>\n<li>[latex]Q[\/latex] = \u2212 (12 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\n<li>[latex]Q[\/latex] = \u22122.71\u00a0\u00d7 10<sup>7<\/sup> J (\u2248 \u22122.7 \u00d7 10<sup>7<\/sup> J)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.2.4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>How much heat is required to convert 250 g of ice at \u221210.0 \u00b0C to steam at 100 \u00b0C?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = Find<\/li>\n<li>[latex]m[\/latex] = 0.25 kg<\/li>\n<li>[latex]L_v[\/latex] = 2.26 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\n<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\n<li>[latex]c_{\\text{ice}}[\/latex]\u00a0= 2100 J\/kg\u00b0C<\/li>\n<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q=mc\\Delta T+mL_f+mc\\Delta T+mL_v[\/latex]<\/li>\n<li>[latex]Q[\/latex] = (0.250 kg)(2100 J\/kg\u00b0C)(0\u00b0C \u2212 \u221210\u00b0C) + (0.250 kg)(3.34 \u00d7 10<sup>5<\/sup> J\/kg) + (0.250 kg)(4187 J\/kg\u00b0C)(100\u00b0C \u2212 0\u00b0C) + (0.250 kg)(2.26 \u00d7 10<sup>6<\/sup> J\/kg)<\/li>\n<li>[latex]Q[\/latex] = 5250 J + 83<span style=\"margin-left: 0.25em;\">500<\/span> J + 104<span style=\"margin-left: 0.25em;\">000<\/span> J + 565<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\n<li>[latex]Q[\/latex] = 758<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 15.2.5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>How much heat must be extracted to change 454 g of water at 20\u00b0C into ice at \u22126\u00b0C?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Data:<\/p>\n<ul>\n<li>[latex]Q[\/latex] = Find<\/li>\n<li>[latex]m[\/latex] = 0.454 kg<\/li>\n<li>[latex]L_f[\/latex] = 3.34 \u00d7 10<sup>5<\/sup> J\/kg<\/li>\n<li>[latex]c_{\\text{ice}}[\/latex] = 2100 J\/kg\u00b0C<\/li>\n<li>[latex]c_{\\text{water}}[\/latex] = 4187 J\/kg\u00b0C<\/li>\n<\/ul>\n<p>Solution:<\/p>\n<ul>\n<li>[latex]Q=mc\\Delta T-mL_f+mc\\Delta T[\/latex]<\/li>\n<li>[latex]Q[\/latex] = (0.454 kg)(2100 J\/kg\u00b0C)(\u22126\u00b0C \u2212 0\u00b0C) \u2212 (0.454 kg)(3.34 \u00d7 10<sup>5<\/sup> J\/kg) + (0.454 kg)(4187 J\/kg\u00b0C)(0\u00b0C \u2212 20\u00b0C)<\/li>\n<li>[latex]Q[\/latex] = \u22125720 J \u2212 151<span style=\"margin-left: 0.25em;\">600<\/span> J \u2212 38<span style=\"margin-left: 0.25em;\">000<\/span> J<\/li>\n<li>[latex]Q[\/latex] = \u2212195<span style=\"margin-left: 0.25em;\">000<\/span> J (\u2248 \u2212200<span style=\"margin-left: 0.25em;\">000<\/span> J)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>How much heat is required to melt 28.6 kg of ice at 0\u00b0C?<\/li>\n<li>How much heat is released when 423 g of steam at 100 \u00b0C is condensed to water at the same temperature?<\/li>\n<li>If 1.85 \u00d7 10<sup>4<\/sup> J of heat is released when 3.85 \u00d7 10<sup>\u22123<\/sup> kg of tungsten is condensed at its boiling point what is the latent heat of vaporization of tungsten?<\/li>\n<li>What mass of ethanol can be solidified by the removal of 9.53 \u00d7 10<sup>4<\/sup> J of heat at its melting point? The latent heat of fusion of ethanol is 1.05 \u00d7 10<sup>5<\/sup> J\/kg.<\/li>\n<li>How much heat is released when 454 g of steam at 100\u00b0C is condensed into water at the same temperature?<\/li>\n<li>A cooler is able to condense 12.0 kg of steam at 100\u00b0C into water at 100\u00b0C? in 2.0 h. Using this same cooler, what mass of water at 0\u00b0C should it be able to freeze into ice at 0\u00b0C in 2.0h?<\/li>\n<li>How much heat must be extracted from a litre of water at 50\u00b0C to turn it into ice at 0\u00b0C?<\/li>\n<li>How much heat is required to convert 1.15 kg of ice 0.00 \u00b0C to water at 21.5 \u00b0C ?<\/li>\n<li>How much heat is required to convert 86.3 g of ice at \u22125.0 \u00b0C to steam at 100 \u00b0C?<\/li>\n<li>How much heat must be extracted to change 500 g of water at 5.0\u00b0C into ice at \u22128.0\u00b0C?<\/li>\n<li>How much heat is required to change 4.0 kg of ice at 0\u00b0C to steam at 100\u00b0C?<\/li>\n<li>How much heat is need to melt the 2.5 \u00d7 10<sup>19<\/sup> kg of ice in Antarctica if we assume an ice temperature of \u221245 \u00b0C? How does this compare to all the energy of the Sun striking the Earth in one year?\u00a0 (Total solar energy incident on Earth is 5.4 \u00d7 10<sup>24<\/sup> J each year.)<\/li>\n<li>If the entire 2 850 000 km3 of Greenland<a class=\"footnote\" title=\"The mass of the Greenland ice sheet is approximately 2.62 \u00d7 1015 kg.\" id=\"return-footnote-189-6\" href=\"#footnote-189-6\" aria-label=\"Footnote 6\"><sup class=\"footnote\">[6]<\/sup><\/a> ice sheet were to melt global sea levels would rise 7.2 m. If we are to assume that the average temperature of this ice is \u221225 \u00b0C, how much energy is needed to turn Greenland\u2019s ice cap into water at 0 \u00b0C?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 15.3.1: Heating Canada\u2019s Homes &#8211; An Exercise in the Geography of Energy<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A typical sized family home consumes about 1500 m<sup>3<\/sup> of natural gas a year to heat (19\u00b0C). This is equivalent to about 57 GJ of energy.<\/p>\n<ol>\n<li>If we were to use wood with an energy density of 1.5 \u00d7 10<sup>7<\/sup> J\/kg, how many kg would we need to heat this house?<\/li>\n<li>If a hectare of forest provides 100<span style=\"margin-left: 0.25em;\">000<\/span> kg of wood, how much wood would be needed to heat all of Canada\u2019s 12 million or so homes?<\/li>\n<li>If we consider that a tree takes roughly 100 years to reach an optimal size for harvesting, what size of forest in Canada would we need to have sustainable heating?<\/li>\n<li>How does the sustainable forest needed for heating compare to Canada\u2019s forest and wooded areas of roughly 400 million hectares?<\/li>\n<li>How does this compare to BC\u2019s forest and wooded areas of 64 million hectares?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 15.3.2: Yearly Melt of Arctic Sea Ice<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-683\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902.png\" alt=\"\" width=\"600\" height=\"475\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902.png 994w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902-300x238.png 300w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902-768x608.png 768w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902-65x51.png 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902-225x178.png 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/02\/20100105_Figure2-e1679943645902-350x277.png 350w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<ol>\n<li>If we assume an average thickness of 2.5 m for this ice being melted and that the ice is at a temperature of \u221250\u00b0C, how much energy is absorbed by this process in a year?<\/li>\n<\/ol>\n<p>Arctic melts around 8 000 000 km<sup>2<\/sup> (2.5 m thick) Heat needed = ______________<\/p>\n<\/div>\n<\/div>\n<h1>Exercise Answers<\/h1>\n<h2>15.1 Specific Heat Capacity<\/h2>\n<ol class=\"twocolumn\">\n<li>1.28 \u00d7 10<sup>7<\/sup> J<\/li>\n<li>\u2212 50<span style=\"margin-left: 0.25em;\">600<\/span> J<\/li>\n<li>78.1 \u00b0C<\/li>\n<li>450 J\/kg\u00b0C<\/li>\n<li>79.4 \u00b0C<\/li>\n<li>8.25 kg<\/li>\n<li>465 J\/kg\u00b0C<\/li>\n<li>6.3 \u00d7 10<sup>4<\/sup> J<\/li>\n<\/ol>\n<h2>15.2 Heat &amp; Phase Changes<\/h2>\n<ol class=\"twocolumn\">\n<li>9.55 \u00d7 10<sup>6<\/sup> J<\/li>\n<li>9.56 \u00d7 10<sup>5<\/sup> J<\/li>\n<li>4.81 \u00d7 10<sup>6<\/sup> J\/kg<\/li>\n<li>0.908 kg<\/li>\n<li>1.03 \u00d7 10<sup>6<\/sup> J<\/li>\n<li>81.2 kg<\/li>\n<li>\u2212 5.43 \u00d7 10<sup>5<\/sup> J<\/li>\n<li>4.87 \u00d7 10<sup>5<\/sup> J<\/li>\n<li>2.61 \u00d7 10<sup>5<\/sup> J<\/li>\n<li>\u2212 1.85 \u00d7 10<sup>5<\/sup> J<\/li>\n<li>1.21 \u00d7 10<sup>7<\/sup> J<\/li>\n<li>1.07 \u00d7 10<sup>25<\/sup> J<\/li>\n<\/ol>\n<h2>15.3.1 Heating Canada\u2019s Homes<\/h2>\n<ol>\n<li>3800 kg<\/li>\n<li>456<span style=\"margin-left: 0.25em;\">000<\/span> ha\/y<\/li>\n<li>45.6 million hectares<\/li>\n<li>[latex]\\dfrac{57}{500}[\/latex] or 11.4%<\/li>\n<li>[latex]\\dfrac{57}{80}[\/latex] or 71%<\/li>\n<\/ol>\n<h2>15.3.2 Yearly Melt of Arctic Sea Ice<\/h2>\n<ol>\n<li>8 \u00d7 10<sup>21<\/sup>\u00a0J<\/li>\n<\/ol>\n<h3>Media Attributions<\/h3>\n<ul>\n<li>&#8220;Energy transition sketch&#8221; from <a href=\"https:\/\/openstax.org\/details\/books\/college-physics\">College Physics<\/a> by Openstax is licensed under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 licence<\/a>.<\/li>\n<li>&#8220;<a href=\"https:\/\/nsidc.org\/arcticseaicenews\/2010\/01\/\">Arctic Sea Ice Extent January 2010<\/a>&#8221; courtesy of the <a href=\"https:\/\/nsidc.org\/about\/data-use-and-copyright\">National Snow and Ice Data Center<\/a>, University of Colorado, Boulder.<\/li>\n<\/ul>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-189-1\">In Fahrenheit, Absolute Zero is defined as \u2212459.67\u00b0F <a href=\"#return-footnote-189-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-189-2\">Benjamin Thompson (Count Rumford) has been quite entertaining for historians to research due to his military, political and amorous adventures. <a href=\"#return-footnote-189-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-189-3\">Count Rumford recorded the amount of water in the barrel to be 2 1\u20444 wine gallons. <a href=\"#return-footnote-189-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-189-4\">Reference - Thermodynamic System: https:\/\/en.wikipedia.org\/wiki\/Thermodynamic_system <a href=\"#return-footnote-189-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><li id=\"footnote-189-5\">Black\u2019s discoveries arose from his work for producers of Scotch whisky in search of the ideal quantity of fuel and water for distillation purposes. <a href=\"#return-footnote-189-5\" class=\"return-footnote\" aria-label=\"Return to footnote 5\">&crarr;<\/a><\/li><li id=\"footnote-189-6\">The mass of the Greenland ice sheet is approximately 2.62 \u00d7 10<sup>15<\/sup> kg. <a href=\"#return-footnote-189-6\" class=\"return-footnote\" aria-label=\"Return to footnote 6\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":125,"menu_order":15,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-189","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":21,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/189\/revisions"}],"predecessor-version":[{"id":1177,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/189\/revisions\/1177"}],"part":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/189\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/media?parent=189"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapter-type?post=189"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/contributor?post=189"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/license?post=189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}