An air pump has a cylinder $0\mathrm{.}290$ m long with a movable piston. The pump is used to compress air from the atmosphere$($at absolute pressure $1\mathrm{.}01$ x $10^5$ Pa$)$ into a very large tank at $3\mathrm{.}90$ x $10^5$ Pa gauge pressure. $($For air, Cv $=20\mathrm{.}8$J$/$mol$.$K$.)$