Problem $3(10$ points$)-$ Internal Energy and Specific Heats

A piston$-$cylinder assembly contains $2$ kg of nitrogen gas $($N$2).$ The gas expands from an initial state

where $T_1=800K$ and $P_1=3$ bar to a final state where $P_2=1$ bar. During the process the pressure and

specific volume are related by $P{v}^2=$ constant. Please draw a schematic and list the necessary

assumptions, and always start with the general form of balance equations. Determine the heat transfer

during the process in kJ$,$ using

A$.$ a constant specific heat evaluated at $300$ K ;

B$.$ a constant specific heat evaluated at $800$ K ;