The Carnot efficiency limit shows the maximum efficiency of a heat engine as:
\begin{align}
\eta & = 1-\frac{T_C}{T_H}
\end{align}
I have often heard comments that $ T_H $ is the temperature limit of the materials used in the particular engine one is working with. Although this may be useful for someone designing a particular engine, I'm wondering what $ T_H $ stands for theoretically. As an example, if I am using gasoline or diesel for fuel, would the theoretical value of $ T_H $ correspond to the adiabatic flame temperature for those fuels? Again, I am not concerned at the present time if that temperature melts all the engine parts, I am interested in what theoretical efficiency limits I can achieve with particular fuels and compression ratios.
This leads me to a second question. If I use the adiabatic flame temperature for a particular fuel as my $ T_H $, I would like to use a $ T_H $ based on the adiabatic temperature of that fuel at different compression ratios. Does anyone know of a resource where I can find the adiabatic flame temperatures of, lets say gasoline or diesel, at different compression ratios? I am looking for a table with various temperatures so I don't have to do the math for each theoretical fuel or compression ratio.
Thanks for considering this question 🙂
Best Answer
In a Carnot cycle, a gas does work while its temperature lowers. If this is done irreversibly you get the maximum theoretical efficiency (constant entropy).
Real engines try to approach this but fail. But yes, when the thermal ratio (input/output) is greater you will get greater efficiency. Thus the drive for materials that can withstand high temperatures in the first stage of gas turbines , for example.
You can in principle improve the temperature at the input by increasing the fraction of oxygen in the air being combusted - if you don't have to heat nitrogen you can get a hotter flame, or if you like a higher temperature / pressure at the start of your Otto cycle.
Putting "real" numbers on this is the realm of engineering more than physics...