# Explained: The Carnot Limit

Anytime engineers try to design a new kind of heat-based engine or improve on an existing design, they bump up against a fundamental efficiency limit: the Carnot Limit.

The Carnot Limit “sets an absolute limit on the with which can be turned into useful work,” says MIT’s Jane and Otto Morningstar Professor of Physics Robert Jaffe, who co-teaches a course on the physics of energy. If engineers are faced with redesigning an engine that is 35 percent efficient, it makes a big difference whether the maximum possible efficiency of such an engine is 50 percent — in which case it may not be feasible to try to push it further — or 80 percent, in which case there is a significant margin for improvement.

Nicolas Léonard Sadi Carnot, who was born in France in 1796 and lived for only 36 years, deduced this limit. His insights into the nature of heat, and the limitations on machines that use heat, had an impact that lasts to this day. What makes his accomplishments all the more remarkable is the fact that the nature of heat itself was not understood until long after Carnot’s death. At the time of his research, scientists still subscribed to the later-discredited “caloric” theory of heat, which held that an invisible fluid of that name carried heat from one object to another.

Carnot’s 1824 book “Reflections on the Motive Power of Fire” laid out a set of principles that, in some cases, are still widely used. One of those is the Carnot Limit (also known as Carnot efficiency), which is given by a simple equation: the difference in temperature between the hot working fluid — such as the steam in a power plant — and its cooled-off temperature as it leaves the engine, divided by the temperature in degrees Kelvin (that is, degrees above absolute zero) of the hot fluid. This theoretical efficiency is expressed as a percentage, which can be approached but never actually reached.

At the time of Carnot’s work, the best steam engines in the world had an overall efficiency of only about 3 percent. Today, conventional steam engines can reach efficiencies of 25 percent, and gas-fired turbine steam generators in power plants can reach 40 percent or more — compared to a Carnot Limit, depending on the exact heat differences in such plants, of about 51 percent. Today’s car engines have efficiencies of 20 percent or less, compared to their Carnot Limit of 37 percent.

Since the limit on efficiency is based on the temperature difference between the heat source and whatever is used to cool the system — usually outside air or a supply of water — it is clear that the hotter the heat source, the higher the possible efficiency. So, for example, Jaffe explains, “a fourth-generation nuclear reactor that heats steam to 1200 degrees Celsius uses a given amount of energy far more efficiently than a geothermal energy source that employs steam at 120 degrees Celsius.”

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Turning heat to electricity... efficiently

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May 19, 2010
This dovetails with Wei Dai's thesis that advanced civilizations will live near black holes, because they will need the incredibly low temperatures that black holes enable: http://weidai.com...oles.txt

May 19, 2010
The matter orbiting and flowing into black holes is extremely hot. By the time all the surrounding matter is consumed into black holes, so that one could get "near", ... the gods would have become quit bored with their experiment anyway.

May 19, 2010
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May 19, 2010
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May 19, 2010

"The scientists who are caught up in the laws and limits placed upon them from the past are no longer scientists, they are philosophers."

Cheers from Oz.

Actually, no they would be called engineers. As an engineer I can't ignore these common sense laws when I decide whether or not it is worth the time, effort, and money to increase an engine's efficiency. My boss would fire me for not using simple concepts to get a handle on the cost-to-benefit ratio of a project.

May 20, 2010
Although I accept the Carnot Limit as a value for research and a place of argument and discussion, I find it intriguing that no advances in technology or research has happened since 1824.

Wrong wrong very wrong. What is amazing is that you said that. Just because we are advancing all the time at every level of technology does not mean we can break fundamental principles whenever we want. We may not understand why something is the way it is but that does not make it different.

Furthermore, Whether we believe Mr Carnot got it right or not makes no difference to scientists or engineers who will always do the best they can with what they have. It is amazing that Mr Carnot got it right so long ago in specifying a principle which still holds true today. Not because we are afraid to test it but because no one has been able to prove it wrong.

May 20, 2010
This is another explanation of why the need for increased energy flux density to support the world's growing population mandates next generation nuclear energy development and increasing thermonuclear fusion energy research.

May 20, 2010
This shows why it is of fundamental importance to research VASIMR engines.

May 20, 2010
I always wondered why we still use thermal energy for creating a torrent of electrical energy. Is it the only way?

May 20, 2010
The matter orbiting and flowing into black holes is extremely hot. By the time all the surrounding matter is consumed into black holes, so that one could get "near", ... the gods would have become quit bored with their experiment anyway.

Yeah, for a distant observer it would appear to take the remaining lifetime of the universe to get "near" enough to do anything.

May 20, 2010
I always wondered why we still use thermal energy for creating a torrent of electrical energy. Is it the only way?

Because coal, oil, natural/ gas, and nuclear reactions are an efficient, cheap, and available source of low entropy. Keep in mind, things like solar panels are subject to thermodynamic limitations as well.

May 21, 2010
I always wondered why we still use thermal energy for creating a torrent of electrical energy. Is it the only way?

We will in the future skip the steam cycle via MHD.

May 21, 2010
While a car engine can be 20% eff in accelerating, that is the only time it is. Average energy eff of a car is around 7% because it is rarely used in it's eff mode.

Since EV's are 20-60% eff depending on the electric source they will be the future.

May 22, 2010
It is my understanding that the Carnot limit applies only to single-cycle systems. The effect of this is that the moment you put the exhaust heat of that system back into the system to do more work, the Carnot limit principle no longer applies. Which, for example, means that internal combustion engines with added turbochargers can theoretically go above the regular Carnot limit in terms of efficiency.

I guess that at this point the return cycle is included in the equation, so it really doesn't matter much. However, I feel that it is a bit misleading to not mention explicitly that the Carnot limit only applies to a single cycle in such a heat system. Case in point; while it may be true that the best steam engines only have efficiencies of up to about 40%, that is a lie of omission because by running steam engines in series you can get far higher efficiencies - and it has been done to great effect in the past, with maximum total efficiencies of well over 80% in existing engines.

May 23, 2010
.....by running steam engines in series you can get far higher efficiencies

I don't think that is right, because any engine in series can just be considered as one engine (just put a box around it), and Carnot principal (diff between in/out heats) would still apply as is.

@Jerry, I agree but I don't think the Carnot principal applies to electric fuel cells.

May 23, 2010

"The scientists who are caught up in the laws and limits placed upon them from the past are no longer scientists, they are philosophers."

Cheers from Oz.

Actually, no they would be called engineers. As an engineer I can't ignore these common sense laws when I decide whether or not it is worth the time, effort, and money to increase an engine's efficiency. My boss would fire me for not using simple concepts to get a handle on the cost-to-benefit ratio of a project.

I gave you five stars on that one! Engineers are not to be theorizing, they are to build things that function by utilizing known sets of formula, materials, equations, etc.

Engineers are also trained specifically NOT to theorize, so that type of 'personality' tends to become the professor and the student -in engineering circles.

The engineer must remember that his 'laws' do not apply when speculation is the game. Thus, in theoretical musing, all 'laws' revert to their TRUE STATE, which is ~THEORY~.