Problem $3$

A gas contained within a piston$-$cylinder assembly, initially at a volume of $0\mathrm{.}1$ m$3,$ undergoes a constant$-$pressure expansion at $2$ bar to a final volume of $0\mathrm{.}12$ m$3,$ while being slowly heated through the base. The change in internal energy of the gas is $0\mathrm{.}25$ kJ$.$ The piston and cylinder walls 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 the gas, in kJ$,$ and

b$)$

the heat transfer between the system and its surroundings, in kJ$.$