Hey, my Physics Professor showed me a Proof of the Carnot Limit!

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Nope, your professor showed you an EXAMPLE of a limit. Odds are it was actually a Pressure Ratio Limit. And there are counter examples to both.

Temperature Ratio
Temperature Ratio Limit
Carnot Limit

First, there is an obligation to Sadi Carnot to acknowledge this did not originate with him, although his name is on it.

Most Limits on machines are imposed by the Pressure Envelope. To the extent there are actual limits on actual machines, it is typically a ratio of the Pressure Envelope to the Pressure inside the machine. That is, the piston stops expanding when the pressures become equal.

In many cases, with Air engines, this is also the same as the ratio of the temperatures. That's because the air inside the machine is at the same density as the air outside the machine at some point in the cycle.

Why? Because the air you breath is at the same temperature, density and pressure as the air you breath, put inside a machine. Inside a machine being at 1 atmospheric unit of pressure, and the same density, means its also the same temperature as the outside air.

Change the material, change the density, the limits track the pressure ratios, not the temperature ratios.

An actual Temperature Ratio Limit

A recycling engine can run into an actual temperature limit.

This occurs when there is sufficient energy for something from two sources at the same temperature Only one source may be used in the simplest design.

Here is an honest Temperature Limit example, Naive Recycling.

Here is a counter-example showing the System Limits which are based on Pressure Ratios, not Temperature Ratios, Steam Recycling. Efficiencies in this counter-example clearly exceed the temperature ratio.

Point being, showing examples of systems which apparently have a Temperature Ratio Limit, does not prove it is a fundamental universal limit. One counter-example is sufficient to show the limit only applies to a particular engine design, or class of engines.

The one and only absolute limit, is that the total energy you get out, will equal the total energy you put in.