Why can't we make Carnot heat engine in real life?

Question

Question is obvious: Why can't we make Carnot heat engine in real life? I read Wikipedia and Fundamentals of Physics (Halliday) but I haven't found anything on my question. There are explanations about formulas and how it works but no obvious answer why it can't be made.

Answer 1

A Carnot engine has to be perfectly reversible. This means zero friction, and perfect thermal conductivity between reservoirs^*.

In practice neither of these things are possible so you will only ever get "close".

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^{* As was pointed out by David White, reversibility requires zero temperature difference between the reservoirs; since the flow of heat is proportional to thermal gradient, an infinitesimal temperature difference implies infinitesimal heat flow, and infinite time per cycle; this is one more reason why the perfect heat engine is thermodynamically out of reach}

Answer 2

As Floris points out the Carnot engine has to be perfectly reversible.

So, for example, the isothermal expansion step requires the resistance to the expansion of the gas to be always just a little bit less than the pressure of the gas inside the cylinder or engine. The pressure drops during the expansion and so the force pushing back on the gas must drop in exactly the same way. If the force pushing back on the gas is higher than this then gas will be compressed. If the pressure is significantly lower then the gas will expand rapidly and its temperature will drop.

Similarly the force compressing the gas in the isothermal compression would have to be just enough to slowly compress the gas - and slowly increase with time.

In a real engine the resistance to motion (= pressure exerted on gas) cannot be controlled in this way and so the Carnot cycle cannot be reproduced in a real engine.

Answer 3

• $TS$ diagram. Changing $PV$ and $T$ while keeping $S$ constant is an engineering conundrum.

• $PV$ and $T$ are measurable and controllable engineering parameters. $S$ is not measurable dependent (on the other three) value.

• $P$, Pressure, can be constant by the use of a constant pressure vessel, such as a boiler, air tank or water tower.

• $V$, Volume, can be held constant by not moving the Piston until other system processes are in position.

• $T$, Temperature, can be held constant by having a large heat sink, such as a fire, the atmosphere, or water supply (lake, river or tank). Technically two heat sinks.

• $S$, Enthalpy, has no direct means of being held constant. $P$ and $V$ would need to go through some difficult changes to keep $S$ constant, while absorbing the expelled heat from the high constant $S$ stroke through some sort of regenerator, plus any extra heat absorbed from the constant high T heat source.

The opposite $PV$ changes would need take place on the heat rejection high $S$ stroke and rejection to the constant low $T$ sink.

It does get worse than that simplified explanation.

No one has discovered how to keep $S$ constant during those two strokes.

There is really no need to, as there are several other cycles that have Carnot efficiency, such as the Sterling, Ericsson, and Rankin with reheat. That leads engineers towards other cycles rather than ponder the complexities of constant $S$ heat transfer.

Answer 4

I lied above. I apologise. Entropy, S, is held constant by the adiabatic condition, also known as good insulation.

No engine has been built using the cycle named in honor of Carnot because two parts of the cycle require total insulation. And two require conduction with one of either the hot or the cold sinks.

Visualize a sealed piston chamber where you:

1. Open an insulating curtain letting heat in while expanding the gas.
2. Closing the curtain and expanding it some more.
3. Opening a second insulating curtain to let heat out, while compressing the gas.
4. Closing the curtain and compressing it some more. Repeat.

The engine Carnot described was frictionless and adiabatic. He was trying to separate heat efficiency from mechanical efficiency. People later made up magic perfect cycles for the practical real world engines running at those historic times. They then extrapolated to create other cycles, the honorary Carnot name was given to the mythical engine Carnot described in his thought exercise. The cycle and his description are somewhat different. There is more latitude in his description, than the cycle permits.

Most of those magic cycles have real engines that approximate them. The Carnot doesn't. The "why", I think, boils down to how to get a cylinder to conduct heat through it, while then becoming an insulator.

It may be possible to build an engine that approximates a Carnot cycle. It would be fun to do so, but it probably won't be very practical. It certainly won't perfectly match his description.

A good read is: The Evolution of the Heat Engine, by Ivo Kolin

https://www.amazon.com/Evolution-Heat-Engine-Ivo-Kolin/dp/0965245527

Answer 5

Even if we have no frictional loss, according to$P=\frac{Constant}V$ at isothermal, and $P=\frac{Const}{V^{\gamma}}$ at adiabatic, these relations must be fulfilled automatically (I mean without extra mechanical work or extra information process) for external pressure ($P_{external}=P_{engine cylinder}$) at each value of $V$. These $P$ vs. $V$ relation must be organized by mechanical apparatus with weights, lever arm, pulley blocks and so on, in presence of gravitation, but without electronic processing machine. I can't imagine such an apparatus...

Answer 6

Irreversibility cannot be the answer because after all, NO engines AT ALL can use absolutely reversible procedures: there are no reversible procedures in nature. So not even the Otto machine can really exist.

I think the answer lies in the impossible adiabatic changes (producing Work by only changing the temperature of the gas, cooling it, with no heat exchange) but I am not sure.

Answer 7

As answered previously, the ideal Carnot cycle consists of four reversible processes. To even approach reversibility, each process would have to occur over a very long time.

Any real-world cycle has irreversibility.

For a thermal water-steam working fluid power plant, a Rankine cycle is preferred over a Carnot cycle due to less work required to pump a liquid than to compress a gas, thereby leaving more work from the turbine to be be used outside the cycle to drive the electrical generator.

See a good engineering textbook for the details of cycles (and processes); such as any of the Sonntag and Van Wylen texts on Thermodynamics. The use of feedwater heaters in a regenerative cycle to improve efficiency is very important in real-world power plants.

Answer 8

A Carnot engine can be any efficiency, dependent on the temperature difference. No one has built any ideal engine. Nor has anyone built a Carnot approximation.

The difficulty is in a cylinder that can go from a temperature conducting sink to an adiabatic insulator. No one has figured that out. Also the Carnot cycle has four processes that begin and end with a dwell/(pause, delay). And two are slow/quasi static, and two are adiabatic/quasi instantaneous. The machine would need to operate at two different speeds/RPMs. No one has figured that out either. Lastly the Carnot cycle engine would be low powered and large. Other cycles are better.

The problem is similar to trying to make a Stirling engine using turbo machinery. No one has yet figured out how to conduct heat through a turbine blade into and out of the working fluid.

There is no intrinsic reason it can't be done. The acoustic Stirling engines could be considered acoustic Carnot engines. No regenerator, not displacer no piston. They heat and expand air, expand it some more, cool and compress air, and compress it some more, sort of, kind of, maybe. Approximately. Just waiting for someone to figure out a way to measure an indicator diagram to compare one to the ideal cycles.

Answer 9

As what they said above, carnot engine has to be perfectly reversible. We know the second law of thermodynamics, "The entropy of an isolated subject always increases." But Qapplied = T1*(s4-s1) and Qrejection = T2*(s2-s3) has constant change of entropy, this then violates the second law.

Edit: If are asking why people need to study carnot engine (impossible), it's because it serves as a basic background of all the engines.

Answer 10

Carnots engine cannot be real because $100\%$ efficiency cannot be obtained in real life.

This is because, to achieve $100\%$ efficiency in Carnot's engine the temperature of the sink must be as least as possible. The least possible temperature we can think of is $0$ kelvin. But, in real life we cannot achieve a temperature of $0$ kelvin. Hence temperature of the sink cannot be maintained at $0$ kelvin, so carnot's engine is not possible practically.