Problem $2(60$ pt$).$ One kmole $(N)$ of argon gas at $T_1=300K$ is initially confined to half

of an insulated and stationary rigid tank. The other half is evacuated. The volume $($V$)$ in

each half is $0\mathrm{.}2m^3.$ The partition between the two halves is removed, and the argon

expands to fill the entire tank. Assume that the constant volume heat capacity for argon

under ideal gas conditions is $(\frac{3}{2})R.$

$(10$ pt$)$ What is the energy balance for this process?

$(10$ pt$)$ What is the appropriate departure function to be used with the van der Waals

equation of state for this process?

$(30$ pt$)$ Calculate the final gas temperature, $T_2(K),$ assuming that argon is a real gas. Use

the van der Waals equation of state in your calculations. For argon, the van der Waals

constants are $a=0\mathrm{.}1355J\frac{m^3}{m}ol{e}^2$ and $b=0\mathrm{.}03201$ liter$/$mole$.$ Solve using an integral

from the attached list.

$(10$ pt$)$ Calculate the final gas temperature, $T_2(K),$ assuming argon is an ideal gas.