Heat capacity is the amount of energy (heat) needed to increase temperature of a substance by one degree. It reflects the capacity of the substance to retain heat. As defined, heat capacity has only a limited application since it is extensive property i.e. depends on mass of the substance. In Physics, specific heat capacity, which is the heat capacity normalized to the unit of mass, is commonly used. Consider a specific example. Calculate both heat capacity and specific heat capacity, if energy, required to increase temperature of an aluminum bar (500g) from 298 to 320 K, is 9900 J.
Subtract temperature of the initial state from temperature of the final state to calculate temperature difference dT: dT=T2-T1. dT= 320-298=22 K
Divide the heat energy amount Q by temperature difference dT to calculate heat capacity Ct. Ct=Q / dT Ct=9900 J / 22 K=450 J/K.
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Divide heat energy amount Q by temperature difference dT and the mass m. Or divide heat capacity Ct(Step 2) by the mass m to calculate specific heat capacity C. C = Q / (dT_m) = Ct/m C=9900 J / (22 K_ 500 g) = 450 J/K / 500g=0.9 J/Kg.