= Isobaric-isochoric-adiabatic heat engine
Consider an ideal-gas cycle with constant heat-capacity ratio $\gamma>1$: expand isobarically from $V_1$ to $rV_1$, cool isochorically, then compress reversibly and adiabatically to the initial state. With $P_*=p_1V_1=nRT_1$, closure gives $T_2=rT_1$ and $T_3=r^{1-\gamma}T_1$. The <heat> input is $Q_h=\gamma P_*(r-1)/(\gamma-1)$ and the rejected <heat> magnitude is $Q_c=P_*(r-r^{1-\gamma})/(\gamma-1)$. Thus $\eta=1-(r-r^{1-\gamma})/[\gamma(r-1)]$. Reservoir temperatures determine feasibility and <entropy> generation but need not coincide with the gas temperatures at heat-exchange endpoints.
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