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$(1)du=cvdT+[T(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}})v-p]dv$

$($a$)$ th $=cpd+V[V-T(\frac{\text{d}\text{e}\text{l}*}{\text{d}\text{e}\text{l}}{)}^2]dp$

$(1$i$)ds=\frac{cp}{T}dT-(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}})pdp$

Note that $u=u(T,v),h=h(T,P)$

$S=S(T,v),S=S(T,P)$