Show [begin{aligned} text { (a) } T mathrm{~d} s & =c_{p} mathrm{~d} T-Tleft(frac{partial v}{partial T} ight)_{p} mathrm{~d} p text { (b) } T mathrm{~d}

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\[\begin{aligned}
\text { (a) } T \mathrm{~d} s & =c_{p} \mathrm{~d} T-T\left(\frac{\partial v}{\partial T}\right)_{p} \mathrm{~d} p \\
\text { (b) } T \mathrm{~d} s & =c_{v}\left(\frac{\partial T}{\partial p}\right)_{v} \mathrm{~d} p+c_{p}\left(\frac{\partial T}{\partial v}\right)_{p} \mathrm{~d} v \\
\text { (c) }\left(\frac{\partial h}{\partial p}\right)_{T} & =v-T\left(\frac{\partial v}{\partial T}\right)_{p} .\end{aligned}\]