Carbon monoxide $($CO$)$ contained in a piston$-$cylinder arrangement, initially at $6\mathrm{.}5$ bar and $452$ K$,$ undergoes an expansion to a final temperature of $263$ K $,$ during which the pressure$-$volume relationship is $\backslash (\backslash$mathrm$\{$pV$\}^\{1\mathrm{.}2\}=\backslash )$ constant. Assuming the ideal gas model for the CO $,$ determine the work in $\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$