$[20$ marks$]$

QA$7.$ Integrate the Clapeyron equation for vapour$-$liquid equilibrium assuming that

the liquid molar volume is negligible compared to the vapour molar volume,

and that the vapour is well described by the virial expansion below, with

coefficient $B=-0\mathrm{.}045$ bar ${?}^{-1}$ :

$Z=1+BP$

Use the expression you obtained to estimate the boiling temperature of

water at $7$ bar, making use of the fact that water boils at $T=99\mathrm{.}6C$ at

$P=1$ bar. The enthalpy of vapourisation of water over the relevant range of

conditions can be considered constant and equal to $38\mathrm{.}9kJmo{l}^{-1}.$

$[30$ marks$]($the answer should be $430\mathrm{.}2$K$)$