<Dd> (∂ U ∂ T) V = (∂ Q ∂ T) V = C V, (\ displaystyle \ left ((\ frac (\ partial U) (\ partial T)) \ right) _ (V) = \ left ((\ frac (\ partial Q) (\ partial T)) \ right) _ (V) = C_ (V),) </Dd> <Dd> (∂ H ∂ T) P = (∂ Q ∂ T) P = C P (\ displaystyle \ left ((\ frac (\ partial H) (\ partial T)) \ right) _ (P) = \ left ((\ frac (\ partial Q) (\ partial T)) \ right) _ (P) = C_ (P)) </Dd> <P> are property relations and are therefore independent of the type of process . In other words, they are valid for any substance going through any process . Both the internal energy and enthalpy of a substance can change with the transfer of energy in many forms i.e., heat . </P> <P> Measuring the heat capacity, sometimes referred to as specific heat, at constant volume can be prohibitively difficult for liquids and solids . That is, small temperature changes typically require large pressures to maintain a liquid or solid at constant volume, implying that the containing vessel must be nearly rigid or at least very strong (see coefficient of thermal expansion and compressibility). Instead, it is easier to measure the heat capacity at constant pressure (allowing the material to expand or contract freely) and solve for the heat capacity at constant volume using mathematical relationships derived from the basic thermodynamic laws . Starting from the fundamental thermodynamic relation one can show that </P>

Molar heat capacity at constant volume and constant pressure