Problem $1\mathrm{.}5$

For an ideal gas

$P=f(T,V)=\frac{nRT}{V}$

Since $T$ and $V$ are state definers, $P$ may be viewed as a state function.

a$.$ Write an expression for $dP,$ in the form of Equation $1\mathrm{.}11.$

b$.$ Then show that the cross derivatives are equal, as predicted by Equation $1\mathrm{.}12.$

c$.,$ Now show that the total change in $P$ is path independent $($Equation $1\mathrm{.}13)$ We will choose the following paths for $1$ mole of gas:

$\backslash$table$[[$State $1,V=20L,T=300K$