{"id":722,"date":"2018-03-20T15:38:13","date_gmt":"2018-03-20T15:38:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-orgbiochemistry\/?post_type=chapter&p=722"},"modified":"2018-08-14T15:55:36","modified_gmt":"2018-08-14T15:55:36","slug":"7-2-heat","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-monroecc-orgbiochemistry\/chapter\/7-2-heat\/","title":{"raw":"7.2 Heat","rendered":"7.2 Heat"},"content":{"raw":"
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Learning Objectives<\/h3>\r\n
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  1. Relate heat transfer to temperature change.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
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    Heat is a familiar manifestation of energy. When we touch a hot object, energy flows from the hot object into our fingers, and we perceive that incoming energy as the object being \u201chot.\u201d Conversely, when we hold an ice cube in our palms, energy flows from our hand into the ice cube, and we perceive that loss of energy as \u201ccold.\u201d In both cases, the temperature of the object is different from the temperature of our hand, so we can conclude that differences in temperatures are the ultimate cause of heat transfer.<\/p>\r\n

    Suppose we consider the transfer of heat from the opposite perspective\u2014namely, what happens to a system that gains or loses heat? Generally, the system\u2019s temperature changes. (We will address a few exceptions later.) The greater the original temperature difference, the greater the transfer of heat, and the greater the ultimate temperature change. The relationship between the amount of heat transferred and the temperature change can be written as<\/p>\r\nheat \u221d \u0394T<\/em><\/span><\/span>\r\n

    where \u221d means \u201cis proportional to\u201d and \u0394T<\/em> is the change in temperature of the system. Any change in a variable is always defined as \u201cthe final value minus the initial value\u201d of the variable, so \u0394T<\/em> is T<\/em>final<\/sub> \u2212 T<\/em>initial<\/sub>. In addition, the greater the mass of an object, the more heat is needed to change its temperature. We can include a variable representing mass (m<\/em>) to the proportionality as follows:<\/p>\r\nheat \u221d m<\/em>\u0394T<\/em><\/span><\/span>\r\n

    To change this proportionality into an equality, we include a proportionality constant. The proportionality constant is called the specific heat<\/span><\/strong><\/span>, symbolized by c<\/em>:<\/p>\r\nheat = mc<\/em>\u0394T<\/em><\/span><\/span>\r\n

    Every substance has a characteristic specific heat, which is reported in units of cal\/g\u00b7\u00b0C or cal\/g\u00b7K, depending on the units used to express \u0394T<\/em>. The specific heat of a substance is the amount of energy that must be transferred to or from 1 g of that substance to change its temperature by 1\u00b0. Table 7.3 \"Specific Heats of Selected Substances\"<\/a> lists the specific heats for various materials.<\/p>\r\n\r\n

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    Table 7.3<\/span> Specific Heats of Selected Substances<\/strong><\/h5>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Substance<\/th>\r\nc<\/em> (cal\/g\u00b7\u00b0C)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    aluminum (Al)<\/td>\r\n0.215<\/td>\r\n<\/tr>\r\n
    aluminum oxide (Al2<\/sub>O3<\/sub>)<\/td>\r\n0.305<\/td>\r\n<\/tr>\r\n
    benzene (C6<\/sub>H6<\/sub>)<\/td>\r\n0.251<\/td>\r\n<\/tr>\r\n
    copper (Cu)<\/td>\r\n0.092<\/td>\r\n<\/tr>\r\n
    ethanol (C2<\/sub>H6<\/sub>O)<\/td>\r\n0.578<\/td>\r\n<\/tr>\r\n
    hexane (C6<\/sub>H14<\/sub>)<\/td>\r\n0.394<\/td>\r\n<\/tr>\r\n
    hydrogen (H2<\/sub>)<\/td>\r\n3.419<\/td>\r\n<\/tr>\r\n
    ice [H2<\/sub>O(s)]<\/td>\r\n0.492<\/td>\r\n<\/tr>\r\n
    iron (Fe)<\/td>\r\n0.108<\/td>\r\n<\/tr>\r\n
    iron(III) oxide (Fe2<\/sub>O3<\/sub>)<\/td>\r\n0.156<\/td>\r\n<\/tr>\r\n
    mercury (Hg)<\/td>\r\n0.033<\/td>\r\n<\/tr>\r\n
    oxygen (O2<\/sub>)<\/td>\r\n0.219<\/td>\r\n<\/tr>\r\n
    sodium chloride (NaCl)<\/td>\r\n0.207<\/td>\r\n<\/tr>\r\n
    steam [H2<\/sub>O(g)]<\/td>\r\n0.488<\/td>\r\n<\/tr>\r\n
    water [H2<\/sub>O(\u2113)]<\/td>\r\n1.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
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    Note<\/h3>\r\n

    The proportionality constant c<\/em> is sometimes referred to as the specific heat capacity<\/em> or (incorrectly) the heat capacity<\/em>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    The direction<\/em> of heat flow is not shown in heat = mc<\/em>\u0394T<\/em>. If energy goes into an object, the total energy of the object increases, and the values of heat \u0394T<\/em> are positive. If energy is coming out of an object, the total energy of the object decreases, and the values of heat and \u0394T<\/em> are negative.<\/p>\r\n\r\n

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    Example 2<\/h3>\r\n

    What quantity of heat is transferred when a 150.0 g block of iron metal is heated from 25.0\u00b0C to 73.3\u00b0C? What is the direction of heat flow?<\/p>\r\n

    Solution<\/p>\r\n

    We can use heat = mc<\/em>\u0394T<\/em> to determine the amount of heat, but first we need to determine \u0394T<\/em>. Because the final temperature of the iron is 73.3\u00b0C and the initial temperature is 25.0\u00b0C, \u0394T<\/em> is as follows:<\/p>\r\n\u0394T<\/em> = T<\/em>final<\/sub> \u2212 T<\/em>initial<\/sub> = 73.3\u00b0C \u2212 25.0\u00b0C = 48.3\u00b0C<\/span><\/span>\r\n

    The mass is given as 150.0 g, and Table 7.3 \"Specific Heats of Selected Substances\"<\/a> gives the specific heat of iron as 0.108 cal\/g\u00b7\u00b0C. Substitute the known values into heat = mc<\/em>\u0394T<\/em> and solve for amount of heat:<\/p>\r\nheat = [latex]150.0\\cancel{\\text{ g}}\\times{\\frac{0.108\\text{ cal}}{1\\cancel{\\text{ g}}\\cancel{^\\text{o}\\text{C}}}}\\times{48.3\\cancel{^\\text{o}\\text{C}}}[\/latex] = 782 cal\r\n

    Note how the gram and \u00b0C units cancel algebraically, leaving only the calorie unit, which is a unit of heat. Because the temperature of the iron increases, energy (as heat) must be flowing into<\/em> the metal.<\/p>\r\n\r\n<\/div>\r\n

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    Skill-Building Exercise<\/h3>\r\n
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      What quantity of heat is transferred when a 295.5 g block of aluminum metal is cooled from 128.0\u00b0C to 22.5\u00b0C? What is the direction of heat flow?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

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      Example 3<\/h3>\r\n

      A 10.3 g sample of a reddish-brown metal gave off 71.7 cal of heat as its temperature decreased from 97.5\u00b0C to 22.0\u00b0C. What is the specific heat of the metal? Can you identify the metal from the data in Table 7.3 \"Specific Heats of Selected Substances\"<\/a>?<\/p>\r\n

      Solution<\/p>\r\n

      The question gives us the heat, the final and initial temperatures, and the mass of the sample. The value of \u0394T<\/em> is as follows:<\/p>\r\n\u0394T<\/em> = T<\/em>final<\/sub> \u2212 T<\/em>initial<\/sub> = 22.0\u00b0C \u2212 97.5\u00b0C = \u221275.5\u00b0C<\/span><\/span>\r\n

      If the sample gives off 71.7 cal, it loses energy (as heat), so the value of heat is written as a negative number, \u221271.7 cal.<\/p>\r\n

      Start with the equation heat = mc<\/em>\u0394T<\/em> and solve for c<\/em> by dividing both sides by m\u0394T:<\/p>\r\n

      [latex]\\frac{\\text{heat}}{\\text{m}\\Delta\\text{T}}=\\frac{\\text{mc}\\Delta\\text{T}}{\\text{m}\\Delta\\text{T}}[\/latex]<\/p>\r\nTherefore, [latex]\\text{c}=\\frac{\\text{heat}}{\\text{m}\\Delta\\text{T}}[\/latex]\u00a0\u00a0 and, plugging in the numbers, [latex]\\text{c}=\\frac{-71.7\\text{ cal}}{\\left(10.3\\text{ g}\\right)\\left(-75.5^\\text{o}\\text{C}\\right)}[\/latex] = 0.923 cal\/go<\/sup>C\r\n

      This value for specific heat is very close to that given for copper in Table 7.3 \"Specific Heats of Selected Substances\".<\/p>\r\n\r\n<\/div>\r\n

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      Skill-Building Exercise<\/h3>\r\n
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        A 10.7 g crystal of sodium chloride (NaCl) had an initial temperature of 37.0\u00b0C. What is the final temperature of the crystal if 147 cal of heat were supplied to it?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

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        Concept Review Exercise<\/h3>\r\n
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          Describe the relationship between heat transfer and the temperature change of an object.<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n

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          Answer<\/h3>\r\n[reveal-answer q=\"433269\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"433269\"]\r\n\r\n1. Heat is equal to the product of the mass, the change in temperature, and a proportionality constant called the specific heat.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n
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          Key Takeaway<\/h3>\r\n<\/div>\r\n
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