Problem # 3 (30 pnt)
Making use of the fact that the entropy S(N, V, E) of a thermodynamic system is an extensive quantity, show
that
$N\left(\frac{\partial S}{\partial N}\right)_{V,E} + V\left(\frac{\partial S}{\partial V}\right)_{N,E} + E\left(\frac{\partial S}{\partial E}\right)_{N,V} = S$
Note that this result implies that $(-N\mu + PV + E)/T = S$, that is, $N\mu = E + PV - TS$.