QUESTION $2$

An ideal gas confined to a piston cylinder assembly goes through the Carnot cycle depicted in figure $1.$ The ideal gas accepts heat from a hot reservoir at $750$ K $,$ the work output from the cycle is $5\mathrm{.}5$ kJ with a cycle thermal efficiency of $36\%.$ Assume that the system has an adiabatic index of $1\mathrm{.}67$ and that $R$ is equal to $3\mathrm{.}02\frac{k}{k}g.$ K$.$

Figure $1.$ Carnot cycle

$2\mathrm{.}1$ Determine the temperature of the cold reservoir to which heat is rejected, and the magnitude of the heat in kJ accepted by the cycle from the hot reservoir.

$2\mathrm{.}2$ Determine the change in entropy experienced by both the hot and cold reservoirs.

$2\mathrm{.}3$ Determine the work done as the gas moves between each pair of points around the cycle.