Q$3$ A gas undergoes a process in a piston$-$cylinder assembly during which the pressure$-$specific

volume relation is $p{V}^{1\mathrm{.}2}=$ constant. The mass of the gas is $0\mathrm{.}18$ kg $.$ The initial pressure and

volume are $p_1=11$ bar,$V_1=0\mathrm{.}03m^3$ and the final pressure is $p_2=27$ bar $.$ The heat

transferred during the process is $2\mathrm{.}2$ kJ $.$ Kinetic and potential energy changes can be neglected.

$($a$)$ Draw the process in a p$-$V diagram.

$($b$)$ Calculate the change in internal energy of the gas in kJ$.$ Specify the assumptions that you

make during calculations.