average energy of × ½ k B T = k B T . In three dimensions, the average energy is k B T . For a mole of a solid, the total energy is U = k B T × N A = RT ( ∵ k B T × N A = R ) Now, at constant pressure, ∆ Q = ∆ U + P ∆ V ≅ ∆ U , since for a solid ∆ V is negligible. Therefore, U R ( .
) Table . Specific and molar heat capacities of some solids at room temperature and atmospheric pressure As Table . shows, the experimentally measured values which generally agrees with Substance Speci"c heat –v (J kg K ) – – Molar speci"c heat (J mol K ) – – predicted value 3R at ordinary temperatures. (Carbon is an exception.) The agreement is known to break down at low temperatures.
Specific heat capacity of water The old unit of heat was calorie. One calorie was earlier defined to be the amount of heat required to raise the temperature of 1g of water by °C. With more precise measurements, it was found that the specific heat of water varies slightly with temperature. Figure .
shows this variation in the temperature range to ° C. Fig. . Variation of specific heat capacity of water with temperature.
For a precise definition of calorie, it was, therefore, necessary to specify the unit temperature interval. One calorie is defined to be the amount of heat required to raise the temperature of 1g of water from . ° C to . ° C.
Since heat is just a form of energy, it is preferable to use the unit joule, J. In SI units, the specific heat capacity of water is J kg – K – i.e. . J g – K – .
The so called mechanical equivalent of heat defined as the amount of work needed to produce cal of heat is in fact just a conversion factor between two different units of energy :