E$4\mathrm{.}2\mathrm{.}5$ The Redlich$-$Kwong model for fluids has a $PvT$ equation of state

$P=\frac{RT}{v-b}-\frac{a}{\sqrt[\phantom{2}]{T}v(v+b)},$

with parameters a and $b,$ which can be estimated from the critical properties. Figure $4\mathrm{.}15$

shows such a sub$-$critical isotherm for benzene. Using only the Redich$-$Kwong equa$-$

tion of state and Figure $4\mathrm{.}15,$ estimate the following quantities at the temperature shown,

$200C$ :

the saturation pressure $P^{at}$;

the liquid and vapor specific volumes, $v^v$ and $v^1$; and

the heat of vaporization, $h^{\text{v}\text{a}\text{p}}(T)=h^{vv}(T)-h^1(T).$

Figure $4\mathrm{.}15$ An isotherm for benzene, $T=200C,$ as predicted by the Redlich$-$Kwong equation of state.quation of state and Figure $4\mathrm{.}15,$ estimate the following quantities at the temperature shown,

$200C$ :

a$.$ find the saturation pressure $P^{at}$;

b$.$ find the liquid and vapor specific volumes, $v^v$ and $v^1$; and

c$.$ find the heat of vaporization, $h^{\text{v}\text{a}\text{p}}(T)=h^{vv}(T)-h^1(T).$

use given Figure $4\mathrm{.}15$ An isotherm for benzene, $T=200C,$ as predicted by the Redlich$-$Kwong equation of state.