A quasi$-$static adiabatic process is performed on a system starting at state $1.$ Indicate the direction in which the system will proceed in the P$$T plane $($i$.$e$.,$ find dP$/$dT$),$ in terms of measurable quantities.

Expected answer and tip. Please shown all work to reach this answer.

$8\mathrm{.}3(\frac{dP}{dT}{)}_S=\frac{C_P}{TV{}_P}>0$ if ${}_P>0$

Consider a $2-$step process: $ds=(\frac{ds}{\text{d}\text{e}\text{l}\text{P}}{)}_{T}dP+(\frac{ds}{dT}{)}_{P}dT.$