$(15$ points$)$ Carbon Dioxide $(C{O}_2)$ is contained within a vertical piston$-$cylinder

assembly. The piston has a mass of $75$ kg and a diameter of $0\mathrm{.}25$ m $.$ The $C{O}_2$

initially occupies a volume of $0\mathrm{.}25m^3.$ The $C{O}_2$ slowly contracts at constant

pressure to a final volume half that of the initial volume. During the process, the

internal energy decreases by $10$ kJ $.$ Neglecting friction between the piston and the

cylinder wall, and assuming that the piston $($not the cylinder$)$ is a good insulator,

determine:

a$.$ the heat transfer to$/$from a system that contains the $C{O}_2$ only.

b$.$ the heat transfer to$/$from a system that contains the $C{O}_2$ and the piston.