$(15$ points$)0\mathrm{.}75$ kg of nitrogen $(N_2)$ gas is contained in a closed, rigid tank fitted with a

spinning paddle wheel. It is initially at $60C$ and $1\mathrm{.}8$ bar $($State $1).$ A process occurs

which raises the pressure of the $N_2$ to $2\mathrm{.}8$ bar $($State $2).$ During this process, the heat

transfer is $8kJ,$ and the power $($due to the spinning paddle wheel$)$ is $W^{}(t)=-0\mathrm{.}02kW,$

which is constant, for $100$ s $.$ A second process brings the $N_2$ to a pressure of $0\mathrm{.}18$ MPa

$($State $3),$ during which there is no work transfer. The system is stationary.

$($a$)$ Find the change in specific internal energy between the initial and final state, $u_3-u_1$

$(k\frac{J}{k}g).$

$($b$)$ What is the temperature of the $N_2$ in the final state, $T_3(C)?$

$($c$)$ Calculate the heat transfer between the $N_2$ and its surroundings for the second

process, $Q_{2-3}(kJ).$