{"id":7377,"date":"2021-06-08T21:55:59","date_gmt":"2021-06-08T21:55:59","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/energy\/"},"modified":"2021-09-24T20:36:03","modified_gmt":"2021-09-24T20:36:03","slug":"energy","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/energy\/","title":{"raw":"Energy","rendered":"Energy"},"content":{"raw":"[latexpage]\r\n
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Define energy<\/i>.<\/li>\r\n \t
  2. Know the units of energy.<\/li>\r\n \t
  3. Understand the law of conservation of energy.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n[pb_glossary id=\"8098\"]Energy[\/pb_glossary] is the ability to do work. Think about it: when you have a lot of energy, you can do a lot of work; but if you\u2019re low on energy, you don\u2019t want to do much work. Work (w<\/i>) itself is defined as a force (F<\/i>) operating over a distance (\u0394x<\/i>):\r\n

    [latex]w = F\\times \\Delta x[\/latex]<\/p>\r\nIn SI, force has units of newtons (N), while distance has units of metres. Therefore, work has units of N\u22c5m (Newton-metres). This compound unit is redefined as a [pb_glossary id=\"8099\"]joule[\/pb_glossary] (J):\r\n

    [latex]\\begin{array}{rrl}\r\n1\\text{ joule}&=&1\\text{ newton}\\cdot \\text{metre} \\\\\r\n1\\text{ J}&=&1\\text{ N}\\cdot \\text{m}\r\n\\end{array}[\/latex]<\/p>\r\nBecause energy is the ability to do work, energy is also measured in joules. This is the primary unit of energy we will use here.\r\n\r\nHow much is 1 J? It is enough to warm up about one-fourth of a gram of water by 1\u00b0C. It takes about 12,000 J to warm a cup of coffee from room temperature to 50\u00b0C. So a joule is not a lot of energy. It is not uncommon to measure energies in thousands of joules, so the kilojoule (kJ) is a common unit of energy, with 1 kJ equal to 1,000 J.\r\n\r\nAn older \u2014 but still common \u2014 unit of energy is the [pb_glossary id=\"8100\"]calorie[\/pb_glossary]. The calorie (cal) was originally defined in terms of warming up a given quantity of water. The modern definition of calorie equates it to joules:\r\n

    [latex]1\\text{ cal}=4.184\\text{ J}[\/latex]<\/p>\r\nOne area where the calorie is used is in nutrition. Energy contents of foods are often expressed in calories. However, the calorie unit used for foods is actually the kilocalorie (kcal). Most foods indicate this by spelling the word with a capital C \u2014 Calorie. Figure 7.1 \"Calories on Food Labels\" shows one example.\r\n\r\n[caption id=\"attachment_7376\" align=\"aligncenter\" width=\"200\"]\"A Figure 7.1 \"Calories on Food Labels.\" This label expresses the energy content of the food, but in Calories (which are actually kilocalories).[\/caption]\r\n\r\n

    \r\n

    Example 7.5<\/p>\r\n\r\n<\/header>\r\n

    \r\n

    Problem<\/h1>\r\nThe label in Figure 7.1 \"Calories on Food Labels\" states that the serving has 38 Cal. How many joules is this?\r\n

    Solution<\/h2>\r\nWe recognize that with a capital C, the Calories unit is actually kilocalories. To determine the number of joules, we convert first from kilocalories to calories (using the definition of the kilo-<\/i> prefix) and then from calories to joules (using the relationship between calories and joules). So:\r\n

    [latex]38\\text{ \\cancel{kcal}}\\times \\dfrac{1,000\\text{ \\cancel{cal}}}{1\\text{ \\cancel{kcal}}}\\times \\dfrac{4.184\\text{ J}}{1\\text{ \\cancel{cal}}}=160,000\\text{ J}[\/latex]<\/p>\r\n\r\n

    Test Yourself<\/h1>\r\nA serving of breakfast cereal usually has 110 Cal. How many joules of energy is this?\r\n

    Answer<\/h2>\r\n460,000 J\r\n\r\n<\/div>\r\n<\/div>\r\nIn the study of energy, we use the term [pb_glossary id=\"8101\"]system[\/pb_glossary]\u00a0to describe the part of the universe under study: a beaker, a flask, or a container whose contents are being observed and measured. An [pb_glossary id=\"8102\"]isolated system[\/pb_glossary]\u00a0is a system that does not allow a transfer of energy or matter into or out of the system. A good approximation of an isolated system is a closed, insulated thermos-type bottle. The fact that the thermos-type bottle is closed keeps matter from moving in or out, and the fact that it is insulated keeps energy from moving in or out.\r\n\r\nOne of the fundamental ideas about the total energy of an isolated system is that is does not increase or decrease. When this happens to a quantity, we say that the quantity is conserved<\/i>. The statement that the total energy of an isolated system does not change is called the [pb_glossary id=\"8090\"]law of conservation of energy[\/pb_glossary]. As a scientific law, this concept occupies the highest level of understanding we have about the natural universe.\r\n
    \r\n

    Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

    \r\n