# Explained: The Carnot Limit

##### May 19, 2010 by David L. Chandler

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.”

Explore further: Could 'Jedi Putter' be the force golfers need?

## Related Stories

#### Turning heat to electricity... efficiently

Nov 18, 2009

(PhysOrg.com) -- In everything from computer processor chips to car engines to electric powerplants, the need to get rid of excess heat creates a major source of inefficiency. But new research points the way ...

#### A traveling-wave engine to power deep space travel

Sep 17, 2004

A University of California scientist working at Los Alamos National Laboratory and researchers from Northrop Grumman Space Technology have developed a novel method for generating electrical power for deep-space travel us ...

#### Lehigh receives grant to reduce cost of carbon capture at coal-fired power plants

Nov 20, 2009

Lehigh University's Energy Research Center (ERC) has been awarded a grant from the U.S. Department of Energy (DOE) to develop methods of recovering and reusing the heat that would be generated by the carbon-dioxide (CO2) compressio ...

#### U.S. scientists develop better heat pump

Jan 18, 2007

U.S. homeowners might soon see their electric bills decreasing thanks to an integrated heat pump system developed by the Oak Ridge National Laboratory.

#### Nuclear cannibals

Mar 04, 2008

Nuclear energy production must increase by more than 10 percent each year from 2010 to 2050 to meet all future energy demands and replace fossil fuels, but this is an unsustainable prospect. According to a report published ...

#### Breakthrough made in energy efficiency, use of waste heat

Apr 01, 2009

Engineers at Oregon State University have made a major new advance in taking waste heat and using it to run a cooling system - a technology that can improve the energy efficiency of diesel engines, and perhaps some day will ...

## Recommended for you

#### Could 'Jedi Putter' be the force golfers need?

Apr 18, 2014

Putting is arguably the most important skill in golf; in fact, it's been described as a game within a game. Now a team of Rice engineering students has devised a training putter that offers golfers audio, ...

#### Technologies for the optical characterization of materials at terahertz frequencies

Apr 18, 2014

The noncontact measurement of material properties using light is used in a wide variety of applications, from airport security scanners to medical x-ray imaging and various analytical techniques. Some of ...

#### Better thermal-imaging lens from waste sulfur

Apr 17, 2014

Sulfur left over from refining fossil fuels can be transformed into cheap, lightweight, plastic lenses for infrared devices, including night-vision goggles, a University of Arizona-led international team ...

#### Information storage for the next generation of plastic computers

Apr 16, 2014

Inexpensive computers, cell phones and other systems that substitute flexible plastic for silicon chips may be one step closer to reality, thanks to research published on April 16 in the journal Nature Communications.

#### With neutrons, scientists can now look for dark energy in the lab

Apr 16, 2014

It does not always take a huge accelerator to do particle physics: First results from a low energy, table top alterative takes validity of Newtonian gravity down by five orders of magnitude and narrows the ...

#### At the origin of cell division: The features of living matter emerge from inanimate matter

Apr 16, 2014

Droplets of filamentous material enclosed in a lipid membrane: these are the models of a "simplified" cell used by the SISSA physicists Luca Giomi and Antonio DeSimone, who simulated the spontaneous emergence ...

##### franl
2.3 / 5 (3) 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
##### Noumenon
2.3 / 5 (6) 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.
##### YankInOz
1.3 / 5 (3) May 19, 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.

I believe that advances in materials and processes allow us to push the Limit and gain greater coefficiency of performance. I know that this may cause consternation and disparagement from some or maybe even many but I also ascribe to the thought:

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

The examples used in this article are at best second law devices wherein you must halve any postulated efficiency because of the maximum efficiency that you can gain from a second law device is 50%.

There are other ways. Those of us who see no box have found ways to dispel these former "laws" through real research and development.

Cheers from Oz.
##### YankInOz
3 / 5 (2) May 19, 2010
And by the way - Msr Carnot would be truly amazed at behaviour of materials in the nano world. Things are really different there. As an example, gold and silver in certain states become magnetic. Who would have thought.

Cheers.
##### fuzz54
3 / 5 (2) 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.
##### jsa09
4.3 / 5 (6) 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.
##### thingumbobesquire
2.3 / 5 (3) 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.
##### probes
3 / 5 (2) May 20, 2010
This shows why it is of fundamental importance to research VASIMR engines.
##### KronosDeret
not rated yet May 20, 2010
I always wondered why we still use thermal energy for creating a torrent of electrical energy. Is it the only way?
##### Shootist
1 / 5 (4) 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.
##### Noumenon
1 / 5 (4) 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.
##### thingumbobesquire
3 / 5 (2) 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.
##### jerryd
not rated yet 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.
##### SantaBJ
not rated yet 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.
##### Noumenon
1 / 5 (4) 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.
##### KBK
1 / 5 (2) 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~.

## More news stories

#### After 13 years, progress in pitch-drop experiment (w/ video)

(Phys.org) —As Cyclone Ita hit northern Australia last weekend, a much slower collision occurred in the world's longest-running lab project, The University of Queensland's Pitch Drop Experiment.

#### How to test the twin paradox without using a spaceship

Forget about anti-ageing creams and hair treatments. If you want to stay young, get a fast spaceship. That is what Einstein's Theory of Relativity predicted a century ago, and it is commonly known as "twin ...

#### 'Dressed' laser aimed at clouds may be key to inducing rain, lightning

The adage "Everyone complains about the weather but nobody does anything about it," may one day be obsolete if researchers at the University of Central Florida's College of Optics & Photonics and the University ...

#### Researchers find tin selenide shows promise for efficiently converting waste heat into electrical energy

(Phys.org) —A team of researchers working at Northwestern University has found that tin selenide (SnSe) has the highest Carnot efficiency for a thermoelectric cycle ever found, making it potentially a possible ...

#### Micro-macro entangled 'cat states' could one day test quantum gravity

(Phys.org) —In Schrödinger's famous thought experiment, a cat's quantum state becomes entangled with the quantum state of a decaying nucleus, resulting in the odd situation that the cat is both alive and ...

#### Making graphene in your kitchen

Graphene has been touted as a wonder material—the world's thinnest substance, but super-strong. Now scientists say it is so easy to make you could produce some in your kitchen.

#### Review: With Galaxy S5, Samsung proves less can be more

Samsung Electronics Co. has produced the most formidable rival yet to the iPhone 5S: the Galaxy S5. The device, released over the weekend, is the fifth edition of the company's successful line of Galaxy S ...

#### Bulletproof nuclei? Stem cells exhibit unusual absorption property

Stem cells – the body's master cells – demonstrate a bizarre property never before seen at a cellular level, according to a study published today from scientists at the University of Cambridge. The property ...

#### Study casts doubt on climate benefit of biofuels from corn residue

Using corn crop residue to make ethanol and other biofuels reduces soil carbon and can generate more greenhouse gases than gasoline, according to a study published today in the journal Nature Climate Change.

#### 4.5 million smartphones were lost or stolen in US in 2013

A report released Thursday said 4.5 million smartphones were lost or stolen in the U.S. last year, up from 2.8 million in 2012.