$4-17$ A frictionless piston$-$cylinder device contains $5$ kg of nitrogen at $100$ kPa and $250$ K $.$ Nitrogen is now compressed slowly according to the relation $\backslash ($ P V$^\{1\mathrm{.}4\}=\backslash )$ constant until it reaches a final temperature of $450$ K $.$ Calculate the work input during this process. Answer: $742$ kJ

FIGURE P$4-17$