= Unregenerated Stirling cycle
{title2=$\eta=\frac{nR(T_h-T_c)\ln r}{nRT_h\ln r+C_V(T_h-T_c)}$}
For an ideal working gas and $r=V_2/V_1>1$, two isotherms at $T_h,T_c$ produce net <work> $nR(T_h-T_c)\ln r$. Without a regenerator, isochoric heating requires additional external <heat> $C_V(T_h-T_c)$, giving the displayed <thermal efficiency>, strictly below <Carnot efficiency>. A perfect reversible regenerator recovers this heat and attains the bound instead. Reversing the unregenerated cycle gives cooling <coefficient of performance> $T_c/(T_h-T_c)-C_V/(nR\ln r)$; positive cooling requires a sufficiently large expansion ratio.
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