Consider the following for a natural gas:

a$.$ Explain how the van der Waals equation of state can be used to

estimate the molar volume of a gas at a pressure, $p,$ and

temperature, $T.$

b$.$ Compressed natural gas $(C{H}_4)$ is stored in a $1\mathrm{.}0m^3$ storage tank.

At a temperature of $-40C$ the pressure of the gas in the tank was

found to be $122\mathrm{.}7$ atmospheres. Estimate $($hint: two or three

iterations will be sufficient$)$ the molar volume of the gas in the

vessel using the van der Waals equation of state and hence

calculate the mass of gas in the vessel.

$40\%$

c$.$ If the temperature of the gas in the tank in b were to rise to $20C,$

determine the pressure of the gas in the vessel.

$15\%$

d$.$ If it is assumed that $C{H}_4$ behaves as an ideal gas estimate the pressure

of the gas in the vessel for the conditions specified in $c.$

$10\%$

e$.$ Determine the compression factor of $C{H}_4$ for the conditions in $c.$

$15\%$

The van der Waals equation of state is $p=\frac{RT}{(widehat(V))-b}-\frac{a}{(widehat(V^2))}$ where $a=\frac{27R^2{T}_C^2}{64p_c}$

and $b=\frac{R{T}_c}{8p_c}$