# Can IC engines be modeled as Carnot engines?

In the "talk" tab for Wikipedia Heat Engine article, someone is questioning whether an internal combustion engine can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines dont operate on a closed cycle. Fresh air enters and is expelled each cycle. There are some answers there as well, but I'd like to get input from you guys to settle this matter once and for all!

Is it ok to model IC engines as heat engines? And in a wider sence; can you model a solar cell as a heat engine and calculate carnot efficiency with T_c being the air temperature, and T_h being temperature of the sun. (I saw this in a textbook once, I believe.)

https://en.wikipedia.org/wiki/Talk:Heat_engine (section headline: "Internal combustion engines can't be considered heat engines")

• That ‘chemical energy’ gets turned into heat to do work. Commented Jun 19, 2023 at 14:26

The Carnot cycle is 4-stage cycle whose stages are (1) isothermal $$\to$$ (2) isentropic $$\to$$ (3) isothermal $$\to$$ (4) isentropic and then start over again. To a first approximation, the Otto-cycle replaces the two isothermal stages with 2 isochore stages. In the Diesel cycle the higher temperature isothermal is replaced with an isobar, while the lower temperature isothermal is replaced with an isochore stage. Both IC cycles are thermodynamic cycles, just they are not as efficient as the Carnot cycle whose efficiency is, as far as our modern science is concerned, the maximum achievable between two given temperatures.

In the "talk" tab for Wikipedia Heat Engine article, someone is questioning whether an internal combustion engine can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines don't operate on a closed cycle. Fresh air enters and is expelled each cycle. There are some answers there as well, but I'd like to get input from you guys to settle this matter once and for all!

• A heat engine is not necessarily based on an ideal gas, although this is the easiest example to use, and there is also a good reason why Carno used it - because he dealt with steam engines.
• The usual gas analysis applies when we treat the fuel that has already exploded, and thus taken the gaseous form. It is the temperature of this gas and the temperature of the surrounding air that determine the limiting efficiency.
• That fresh air enters in the beginning of the cycle is not relevant, in view of the previous point. Note however, that a non-ideal heat engine does not have to be connected to only one reservoir at a time, although it complicates the analysis, and may even prevent the analysis in terms of quasistatic processes.

Is it ok to model IC engines as heat engines? And in a wider sence; can you model a solar cell as a heat engine and calculate Carnot efficiency with $$T_c$$ being the air temperature, and T_h being temperature of the sun. (I saw this in a textbook once, I believe.)

What makes a solar cell different (in fact simpler) is that it is not performing a cyclic motion, but simply diverts a part of the energy flux flowing from one body to another, transforming it to another type of energy. The actual engine, converting this energy to work in Carno sense is located elsewhere - e.g., the motor supplied by the cell (possibly with intermediary of a battery). In this sense a solar cell can be compared to a water wheel, which turns as a side effect of water running to a lower level. The temperature here is relevant only as much as it determines the mangtitude of the energy flux.

• One has to point out that when Carnot was basically establishing thermodynamics for the first time, he was studying it for the context of steam engines, which are also not closed. He was the first one to realise that the analysis is simpler if he could close the loop, and we have been following him ever since. This means that the cycle being open is but a complication that does not rule out an engine being labelled as a heat engine. Commented Jun 20, 2023 at 3:20
• Also, while things like a solar cell is not in the usual thermal equilibrium, its behaviour necessarily has to obey some, much more complicated, version of thermodynamics. Same thing with lasers, etc. See the link Bob D provided. Commented Jun 20, 2023 at 3:22

,,,can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines don't operate on a closed cycle. Fresh air enters and is expelled each cycle.

Yes it can be modeled as a heat engine even though, in reality, it is not a heat engine in the strictest sense. Specifically it can be modeled as a reversible Otto cycle where the working fluid is an ideal gas. A PV diagram of the cycle is shown in FIG 1 below. A TS diagram for the cycle is shown in FIG 2. For comparison to an ideal gas Carnot cycle, a TS diagram for it is shown in FIG 3.

A real IC engine is obviously not reversible. But by modeling it as a reversible heat engine cycle one can establish and upper limit to the efficiency of the real engine. (Note: FIG 1 shows the intake and exhaust strokes. They have no effect on the theoretical maximum efficiency of the reversible cycle.)

Comparing FIGs 2 and 3 one can see what limits the efficiency of the reversible Otto cycle compared to the Carnot cycle is that all of the heat added and rejected in the Carnot cycle occurs at fixed temperatures, which maximizes the area enclosed (net work done) in the TS diagram for a given maximum and minimum cycle temperature. For the Otto cycle, the addition and rejection of heat occur over a range of temperatures.

Regarding solar cells being modeled as heat engines, you might find the following of interest: What kind of engine is a photovoltaic solar cell?

Hope this helps.