Q$5.$ The critical constants of methane are $P_c=45\mathrm{.}6$atm,$V_c=98\mathrm{.}7c{m}^{3}mo{l}^{-1},$ and $T_c=190\mathrm{.}6K.$ Calculate the van der Waals parameters of the gas and estimate the radius of the molecules.

Q$6.$ A sample consisting of $1\mathrm{.}0$mol of perfect gas molecules with $C{V}_V=20\mathrm{.}8J{K}^{-1}$ is initially at $3\mathrm{.}25$ atm and $310K.$ It undergoes reversible adiabatic expansion until its pressure reaches $2\mathrm{.}50$atm. Calculate the final volume and temperature and the work done.