Nitrogen $\backslash (\backslash$left$(\backslash$mathrm$\{$N$\}\_\{2\}\backslash$right$)\backslash )$ contained in a piston$-$cylinder arrangement, initially at $5\mathrm{.}4$ bar and $439$ K $,$ undergoes an expansion to a final temperature of $300$ K $,$ during which the pressure$-$volume relationship is $\backslash (\backslash$mathrm$\{$pV$\}^\{1\mathrm{.}2\}=\backslash )$ constant. Assuming the ideal gas model for the $\backslash (\backslash$mathrm$\{$N$\}\_\{2\}\backslash ),$ determine the heat transfer in J$/$kg$.$