Problem $3$

A gas contained within a piston$-$cylinder assembly, initially at a volume of $0\mathrm{.}1m^3,$ undergoes a constant$-$

pressure expansion at $2$ bar to a final volume of $0\mathrm{.}12m^3,$ while being slowly heated through the base.

The change in internal energy of the gas is $0\mathrm{.}25kJ.$ 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 $kJ.$

As always, be sure to draw a schematic that identifies a system for analysis and includes the relevant

energy transfers between the system and the surroundings.