# What is the efficiency of an ideal stirling engine?

I learned that the theoretical Carnot cycle has the highest possible efficiency:

$$e=1-\frac{T_{cold}}{T_{hot}}$$

What about the ideal Stirling cycle? Does it also create the Carnot efficiency?

EDIT: in response to the comment below, let us assume we have aStirling engine using a monatomic gas as a heat exchanger, operating between temperatures $$T_{hot}$$ and $$T_{cold}$$, undergoing isochoric heating and cooling at volumes $$V_1$$ and $$V_2$$ respectively. It can be shown that in this case, the efficiency $$\eta$$ is given by
$$\frac{1}{\eta} = \frac{3}{2ln(\frac{V_2}{V_1})}+\frac{T_{hot}}{T_{hot}-T_{cold}}$$.
Now in the idealized limit as $$\frac{V_2}{V_1} \rightarrow \infty$$, then we can see the efficiency tends towards a Carnot efficiency. Of course this is impossible to achieve in practice, but the maximum possible efficiency of a Stirling engine is the Carnot efficiency because the entropy change around the circuit tends towards zero.
• This is totally wrong. Only the Carnot-cycle, isothermal-adiabatic-isothermal-adiabatic has the efficiency of the $1-\frac{T_{low}}{T_{high}}$, for proof see physics.stackexchange.com/questions/300347/… Mar 24, 2023 at 2:31