Relations between Heat Capacities in Pure Real Gases

RELATIONS BETWEEN HEAT CAPACITIES IN PURE REAL GASES 

The heat capacities most frequently measured are those at constant pressure and at constant volume. In this section we obtain expressions for the difference and the ratio of these two heat capacities. 

The heat capacity at constant pressure is defined by the relation 

The total differential of the internal energy in a closed system can be written 

Equation (7-112) can be rewritten, using the formula for implicit differentiation [Eq. (A-10)], in the form 

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