The heat engine shown in Fig. $3$ uses $0\mathrm{.}02$mol of a diatomic gas as the working substance.

$(6pts)($a$)$ Show that $U_{\text{A}\text{B}\text{C}}=0$ by calculating $U_{AB},U_{BC}$ and $U_{CA}.$

$(3$ pts$)($b$)$ In which process is the heat $Q_n$ absorbed by the gas $?$ Explain.

$(3$ pts$)($c$)$ In which process is the heat $Q_c$ rejocted by the gas? Explain.

$(5$ pts$)($d$)$ What is the engine's thermal efficiency.