Problem $5-$ Energy Balance $(10$ pts$)$

A gas contained within a piston$-$cylinder assembly, initially at a volume of $0\mathrm{.}5m^3,$ undergoes a

constant$-$pressure process at $1\mathrm{.}5$ bar to a final volume of $0\mathrm{.}15m^3,$ while being slowly cooled

through the base. The change in internal energy of the gas is $0\mathrm{.}20$ kJ $.$ The piston and cylinder

sidewalls are fabricated from heat$-$resistant materials for thermal insulation, and the piston

moves smoothly in the cylinder without friction. By taking the gas as the system, $($a$)$ find the

work done by or on the gas, in kJ$,$ and $($b$)$ the heat transfer between the system and its

surroundings, in kJ$.$