UCSB Science Line
Sponge Spicules Nerve Cells Galaxy Abalone Shell Nickel Succinate X-ray Lens Lupine
UCSB Science Line
How it Works
Ask a Question
Search Topics
Our Scientists
Science Links
Contact Information
Can the efficiency of a heat engine exceed that of the Carnot cycle?
Question Date: 2013-05-10
Answer 1:

Real heat engines transferring energy between two reservoirs are less efficient than Carnot heat engines. This is a consequence of the fact that real heat engines undergo irreversible processes, and irreversible processes are less efficient (transfer less heat energy for a given temperature). This in turn is because of the second law of thermodynamics, which states that the entropy of an isolated system is always maximized (never decreases) at equilibrium. If an isolated system undergoes an irreversible process, it is being pushed out of equilibrium. The system will maximize entropy in the process to get to its equilibrium state, and thus entropy increases in a system undergoing an irreversible process.

Mathematically for the heat engine, we say:

dS = -Qhot/Thot + Qcold/Tcold
work = -Qhot + Qcold
efficiency = |work|/Qhot
= |-Qhot + Qcold|/Qhot
= 1-Qcold/Qhot
(since work is negative)
now, since dSsystem = 0,
-Qhot/Thot + Qcold/Tcold = 0
which implies that
Qcold/Qhot = Tcold/Thot
efficiency = 1-Tcold/Thot

So the efficiency of your heat engine is limited by the difference in the temperatures of the reservoirs. I hope this helps.

Answer 2:

No, the Carnot cycle places an upper bound on the efficiency of a heat engine. In practice, is it impossible to achieve the reversible expansion and compression required to gain the efficiency of a Carnot engine due to friction and kinetic requirements


Answer 3:

No it cannot. And in fact it is very difficult to get a heat engine even close to the efficiency of the Carnot cycle.

Answer 4:

No, the Carnot cycle is the ultimate thermodynamic limit of the efficiency of a heat engine. Thermodynamics hasn't been violated yet, which is why they are called the "laws" of thermodynamics.

Answer 5:

This is a good question! The Carnot efficiency limit is derived from a theoretical heat engine cycle that includes reversible isothermal (constant temperature) and isentropic (constant entropy or no heat exchange) steps of a gas to generate work. The Carnot efficiency is the ultimate thermodynamic limit on this type of engine. But because we have no current gases or materials that behave perfectly isothermally or isentropically, the efficiencies of real heat engines is always less than the Carnot efficiency. However, this does not mean that *all* engines operate below the Carnot efficiency! For instance, fuel cells can be shown to have a much higher efficiency than that of a Carnot engine at lower temperatures. This is because Carnot limitations only apply to heat engines.

Answer 6:

Nope! It turns out that given a hot and a cold reservoir of given temperatures, a Carnot cycle is the most efficient possible heat engine operating between those reservoirs (this is why Carnot engines are so important in thermodynamics - they give the maximum possible efficiency of a heat engine).

Answer 7:

That's a great question and a very advanced one on the topic of thermodynamics. The short answer to your question is no, the Carnot cycle is the theoretical maximum efficiency of any heat engine, ever. But let me explain why that is the case. So, as you must already know, a heat engine produces useful work by using the energy from some working fluid (it could be air, water vapor, or any other liquid or gas). Energy can come in two forms, either heat or work. When we talk about work here, what we mean in moving something with some amount of force. A car's engine produces work by rotating the wheels against the forces that tend to slow a car down. For the heat engine to produce work, the working fluid must be at some high temperature, hence it has a lot of useful energy. The heat engine then extracts the heat, turning it into useful work (like spinning the shaft of a motor) and then dumps out the working fluid to some cooler source, called a sink (as in fluid is sinking in). At the end of the cycle, the working fluid cannot be cooler than the sink, because the only way to cool the working fluid is for the sink to absorb its heat. Since heat only flows from high temperature things to low temperature things, the working fluid will never get colder than the sink. So basically, the energy available to the heat engine is all the energy in the high temperature working fluid. However, by necessity, the working fluid has to come out at the same temperature as the sink, and so when the working fluid is dumped out, it takes with it some heat energy. The efficiency of the cycle is defined as the amount of useful work that you get out of the system, divided by the amount of energy that you put in originally. You originally put in all the heat at the working fluid's high temperature state. But the work you got out is only the difference between the high temperature state and the sink temperature, so you will never be able to get better than that, and that is described by the Carnot cycle.

But even the Carnot cycle is ambitious, it is a theoretical cycle and will never, and can never exist in real life. In real life there are always losses, due to friction and imperfections. So the theoretical max can never even be reached. Let's look at some real life cycles, like the Otto cycle, which is the principle on which a gasoline car operates. The working fluid is air, taken from outside, the high temperature is provided by the fuel. (It also produces high pressure, but we can ignore that for illustration purposes.) The high temperature air expands, pushing on a piston, which eventually drives the wheels, producing useful work. When the air has pushed the cylinder as much as it can, it is vented out as exhaust. The outside air is the sink in this case. The air can never be vented out at a temperature lower than the outside (because it simply won't cool down that much), and in fact, it is usually vented at considerably higher temperature. Remember that since heat is a form of energy, all the hot are that comes out of the exhaust is just wasted energy. Then new air comes in and the cycle is repeated.

So, indeed, the Carnot cycle is the most efficient cycle because it describes a situation in which you can usefully use all of the energy contained in the working fluid as it moves from high temperature to sink temperature (low temp.), but in reality it is impossible to actually do that. For reasons why, you should look into entropy and the second law of thermodynamics. Entropy is a big subject, but it basically says that energy always spreads out and becomes less useful. Entropy is connected to all types of scientific questions, from how the universe started to why time flows forwards, and not backwards. It's an interesting subject, but too much for this answer.

Thanks for the question.

Click Here to return to the search form.

University of California, Santa Barbara Materials Research Laboratory National Science Foundation
This program is co-sponsored by the National Science Foundation and UCSB School-University Partnerships
Copyright © 2017 The Regents of the University of California,
All Rights Reserved.
UCSB Terms of Use