# Temperatures of the hot source and cold sink in a heat engine

FranzDiCoccio
Hi,
I was just wondering about the efficiency of a cycle that is not Carnot cycle.

In that case one should use $\eta = 1-\left|\frac{Q_{\rm out}}{Q_{\rm in}}\right|$, where $Q_{\rm in}$ and $Q_{\rm out}$ are the amounts of heat absorbed and released during the cycle.

For instance, I guess that in an (ideal) Stirling cycle (isochoric - isothermal expansion - isochoric - isothermal compression) $Q_{\rm in}$ involves the isochoric transformation with increasing temperature and the isothermal expansion, while $Q_{\rm out}$ involves the remaining two transformations.
I quickly browsed online and I actually found something like that.

Now the usual diagram for a generic machine (at least in my textbook) seems to suggest that $Q_{\rm in}$ is absorbed from a heat resevoir at some temperature $T_h$ and $Q_{\rm out}$ released into a heat sink at a lower temperature $T_c<T_h$.
See e.g. this one I found on the web, which is similar to the ones in my textbook

But, in the case of the Stirling cycle, what does it really mean that $Q_{\rm in}=Q_{\rm isothermal}+Q_{\rm isochoric}$ is absorbed "at $T_h$"? It seems to me that this could apply to the isothermal part only, because the heat intake in the isochoric process does not happen at a fixed temperature...

Are all of these diagrams actually referring to a Carnot engine?
Or perhaps this has to do with the fact that any cycle can be decomposed into many Carnot cycles, so ultimately the diagrams assume that the heat exchanges happen at fixed temperatures?

Thanks a lot for any insight.
Franz

mfig
In a Stirling cycle, the only heat added from the hot reservoir is during the isothermal process at ##T_H##, while all the heat rejected to the cold reservoir would take place during the other isothermal process at ##T_L##. The heat interactions during the isochoric processes are internal - i.e., from heat stored in and taken from the regenerator. Heat rejected to the regenerator during the isochoric cooling is absorbed during the iscochoric heating. These heat interactions do not see the thermal reservoirs. Note this assumes the regenerator is 100% efficient.

FranzDiCoccio
Hi mfig,