Heat capacity - Aetherwisp

Heat capacity or thermal capacity $C$ is the amount of heat $Q$ that needs to be absorbed by a body to incur a unit change in temperature $T$ , such that

C=\lim_{ T \to 0 } \frac{\Delta Q}{\Delta T}=\frac{ \partial U }{ \partial T } =T \frac{ \partial S }{ \partial T }

where $U$ is the internal energy and $S$ is entropy. It is an extensive property, with more massive objects having more heat capacity, though it the quantity varies greatly depending on the thermodynamic state of the body and is better represented as the function $C(P,T)$ , with $P$ pressure and $T$ temperature. The entropy-dependent formula is a convenient way to measure entropy differences experimentally, as we can see by inverting the formula:

\Delta S=\int_{T_{1}}^{T_{2}} \frac{C(T)}{T}dT

With an experimental fit of $C(T)$ , we can perform consistency tests on the theory.

The heat capacity also depends on the kind of thermodynamic transformation that's applied onto the body. Different types of transformations are usually denoted with a subscript: $C_{V}$ for constant volume ones, $C_{P}$ for isobaric ones, etc.