Please write a sheet espcially c

$($

a$)$ Derive the equation giving the change in entropy as a function of temperature and pressure. $(5p$

$($b$)$ Write down the coefficient and Maxwell relations for $H=H(S,P).(10$ p$)$

$($c$)$ Compute the change in internal energy $($ unit lt $*atm)$ when $12$ It of Ar gas $($assumed to be ideal$)$ at $273K$ and $1$atm is compressed to $6lt$ with the final pressure equal to $10$atm. $(20$ P$)$

Hint: Get an expression for $U=U(P,V),$ apply it to an ideal gas, and integrate the expression for $dU$ from $(P_i,V_i)$ to $(P_f,V_f).$

$=\frac{1}{V}*(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$

$=-\frac{1}{V}*(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$

$R=0\mathrm{.}0821\frac{lt*atm}{\text{m}\text{o}\text{l}\text{e}*K}=1\mathrm{.}987\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}\text{e}*K}=8\mathrm{.}3144\frac{J}{\text{m}\text{o}\text{l}\text{e}*K}$