= Solution
Use an <ideal gas> to illustrate the <Carnot cycle>, with hot and cold <heat baths> at $T_h=T_2$ and $T_c=T_1$. The four processes are all <reversible thermodynamic processes>. Lettered states below belong only to this illustration; the engine later in the question uses numbered states.
\Image[/past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2022/paper-2-c8-carnot-pv.png]
{title=An ideal-gas Carnot cycle: two isotherms joined by two reversible adiabats}
Starting at $A$, perform the following four stages:
* $A\to B$: <isothermal expansion> at $T_h$. The gas absorbs <heat> $Q_h$ from the hot <heat bath> and does <work>. Its <internal energy> is unchanged, so $Q_h=W_{AB}=nRT_h\ln(V_B/V_A)$.
* $B\to C$: <reversible ideal-gas adiabat> during expansion. Insulation prevents <heat transfer>; <work> done by the gas reduces its <internal energy> and lowers its <temperature> from $T_h$ to $T_c$.
* $C\to D$: <isothermal compression> at $T_c$. <Work> done on the gas is rejected as <heat> $Q_c$ to the cold <heat bath>, with $Q_c=nRT_c\ln(V_C/V_D)>0$.
* $D\to A$: insulated <adiabatic compression>, performed reversibly, raises the <temperature> back to $T_h$ and closes the cycle.
The clockwise enclosed area in the <pressure>-<volume> diagram is the positive net <work> per cycle, $W=\oint p\,dV=Q_h-Q_c$.
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