$($a$)$ Determine the state $($liquid$/$vapour$)$ of benzene at $P=5$ bar and $T=120C$ and $P=0\mathrm{.}5$ bar and $T=120C.$

$($b$)$ Estimate the difference in enthalpy between state bar, $($:$T=120C\}$ and state $=0\mathrm{.}5$ bar, $($:$T=120C\}$ of benzene from the following data:

Latent heat of vaporization at normal bviling point $(353\mathrm{.}2K)=30\mathrm{.}75k\frac{J}{m}ol$;

$T_c=562\mathrm{.}10K$;$P_c=49\mathrm{.}24$ bar

Specific volume of liquid benzene may be assumed to be $9\mathrm{.}0{10}^{-5}\frac{m^3}{m}ol$

$lo{g}_{10}P(mmHg)=6\mathrm{.}88-\frac{1196\mathrm{.}7}{t(oC)+219\mathrm{.}16}$

Equation of state of the gas is given by $Z=\frac{PV}{RT}=1+\frac{BP}{RT}$ where $B=0\mathrm{.}05\frac{L}{g}$mol. $]$

Sketch the path followed for solving the problem on a P$-$v diagram.

$[20+5]$