Problem $1.$ A gas is compressed in a piston$-$cylinder assembly from $p_1=160,V_1=1f{t}^3$ to $p_2=390,$ in a process during which the relation between pressure and volume is $p{V}^{1\mathrm{.}2}=$ constant. The mass of the gas is $0\mathrm{.}4$ lb $.$ During the process, heat transfer from the gas to the surroundings is $2\mathrm{.}1$ Btu. Kinetic and potential energy changes are negligible. For the gas as the system, determine $($a$)$ the final volume in $f{t}^3,($b$)$ the work in Btu, and $($c$)$ apply first law and determine the change in the specific internal energy in Btu$/$lb$.$