Consider a cylinder fitted with a piston that contains $2$mol of $H_{2}O$ in a container at $1000K.$

Calculate how much work is required to isothermally and reversibly compress this gas from $10L$

to $1L,$ in each of the following cases:

$($a$)$ Use the ideal gas model for water.

$($b$)$ Use the Redlich$-$Kwong equation to relate $P,v,$ and $T$ :

$P=\frac{RT}{v-b}-\frac{a}{T^{\frac{1}{2}}v(v+b)}$

where, $a=14\mathrm{.}24J{K}^{\frac{1}{2}}\frac{m^3}{m}o{l}^2$ and $b=2\mathrm{.}11{10}^{-5}\frac{m^3}{m}ol$

$($c$)$ Assuming the gas follows van der Waals EOS $($as opposed to Redlich$-$Kwong$),$ use the

critical point data for water to estimate the van der Waals constants $($ a and $b)$ for water.