Expressions for Heat Capacity

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Homework Statement



Let [itex]C_{X}=T(\partial S/\partial T)_{X}[/itex] with [itex]X=p~or~V[/itex]. Show that [itex]C_{p}-C_{V}=T(\partial S/\partial V)_{T}(\partial V/\partial T)_{p}[/itex].

Homework Equations



[itex]C_{p}-C_{V}=T[(\partial S/\partial T)_{p}-(\partial S/\partial T)_{V}][/itex]

The Attempt at a Solution



I honestly don't know where to start. I looked at some of the Maxwell relations, but no Maxwell relation features conjugate variables in the numerator and denominator of a partial derivative. I'm not sure how what other way I might use to manipulate the thermodynamic variables.
 

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