Ques $3$: The fundamental relation $($f$.$r$.)$ of a particular system is given as:

$S=N{s}_o+NRln[(\frac{U}{U_o}{)}^c(\frac{V}{V_o})(\frac{N}{N_o}{)}^m]$

i$)$ How are $m$ and $c$ related?

ii$)$ Determine $U(T,V,N).$

iii$)$ Determine $P(T,V,N).$