In a piston cylinder assembly, one $\mathrm{kmol}$ of an ideal gas is compressed from an initial state of $200 \: \mathrm{kPa}$ and $400 \:\mathrm{ K}$ to a final state of $1 \: \mathrm{MPa}$ and $400\: \mathrm{ K}$. If the surroundings are at $400 \: \mathrm{K}$, the minimum amount of work (in $\mathrm{kJ} / \mathrm{kmol}$) required for the compression process is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Use: Universal gas constant $\left(R_{u}\right)=8.314 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$
