The virial equation of state for nitrogen is $PV=RT(1+2{10}^{-4}P),[$where $"$P$"$ in atm$].$ One mole of nitrogen gas at $300K$ is isothermally compressed from $V=100$ liers to $V=1$ liter. Calculate $($a$)w$; $($b$)q$; $($c$)G$ for the isothermal compression process, and $($d$)$ fugacity of nitrogen gas at $V=100$ liters and $V=1$ liter.