$($c$)$ Which of the following relations is correct?

A $,(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T=T(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_V+P$

B $,(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T=P(\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{P}}{)}_V-P$

C $,(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T=T(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_V-P$

D $(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T=P(\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{P}}{)}_V+P$

$($d$)$ Which of the following statements is true for a given component at different T and P$?$

A The compressibility factor $Z$ is a constant

B $,T_c$ and $P_c$ are constants

C $T_r$ and $P_r$ are constants

D The Second virial coefficient B is a constant

$($e$)$ Which of the following statements is true for the vapour$/$liquid equilibrium of a mixture?

A For every component, its partial molar entropies in the liquid and vapour phases

are identical.

B For every component, its chemical potentials in the liquid and vapour phases are

identical.

C For every component, its partial molar enthalpy in the liquid and vapour phases

are identical.

D For every component, its fugacity coefficients in the liquid and vapour phases are

identical.