= Temperature-linear pressure and volume-independent heat capacity
{title2=$(\partial C_V/\partial V)_T=T(\partial^2p/\partial T^2)_V$}
For a smooth simple compressible system, $C_V=T(\partial S/\partial T)_V$ and the <Maxwell relation> $(\partial S/\partial V)_T=(\partial p/\partial T)_V$ give $(\partial C_V/\partial V)_T=T(\partial^2p/\partial T^2)_V$. Thus an <equation of state> $p=a(V)T+b(V)$ implies that $C_V$ depends on <temperature> alone within a smooth <phase>. It does not require $C_V$ to be <temperature> <independent>.
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