Heat Associated with a Temperature Change

The heat capacity of a body is defined as the amount of heat required to increase the temperature of the body 1 K. The heat capacity itself may depend on temperature, but we will ignore this complication. For the same reasons that we distinguish between internal energy and enthalpy, we distinguish between heat capacity at constant volume, C_V, and heat capacity at constant pressure, C_P. For pure substances, we often use the molar heat capacity (heat capacity per mole) or the specific heat capacity (heat capacity per gram). This distinction is clear from the units of C: J/K for an entire body, J/mol•K for one mole of a pure substance, J/g•K for one gram of a pure substance.

If a substance of heat capacity C_V J/K is heated or cooled at constant V through a temperature change ΔT, the heat transferred is

  (1.1)            

or at constant P,

       (1.2)          

Example 1

What is the enthalpy change when 100 g of copper is heated from 10°C to 100°C? C_P(Cu) = 0.389 J/g•K.