$(15$ 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 $60\backslash$deg C 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 $8$ kJ$,$ and the power $($due to the spinning paddle wheel$)$ is $()=0\mathrm{.}02,$

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$1$

$($kJ$/$kg$).$

$($b$)$ What is the temperature of the N$2$ in the final state, T$3(\backslash$deg C$)?$

$($c$)$ Calculate the heat transfer between the N$2$ and its surroundings for the second

process, Q$2-3($kJ$).$