the first Tds equation
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Also, in a constant volume process, TdS = dU so that T(∂S∂T)V=(∂U∂T)V=CV. Therefore TdS=T(∂P∂T)VdV+CVdT. This is the first of the TdS equations. dS=(∂S∂P)TdP+(∂S∂T)PdT.
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