Q$4.($a$)$ What is the total kinetic energy of $0\mathrm{.}50$mol of an ideal monatomic gas confined to $8\mathrm{.}0d{m}^3$ at $200$kPa $?$

$($b$)$ Calculate the pressure of nitrogen $($molar mass $=28g*mo{l}^{-1})$ at an altitude $100km$ assuming that sea$-$level pressure is exactly latm and that the temperature of $298\mathrm{.}15K$ is constant?

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.