I always used to think (I don’t know why!) that the efficiency of human (and animal and plant) cells should be equal to or near the efficiency of a Carnot engine or at least should be the highest efficiency among all practical engines. But I wondered when I saw the answers given to this question. They are talking about an efficiency of $18-26\%$. But you can see here that the efficiency of an Otto engine is between $56\%$ and $61\%$. Is there any explanation for this? Which cycle do human cells work with? Can we compare living cells with heat engines at all?

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    $\begingroup$ Is this really physics? $\endgroup$ – John Rennie Jun 29 '16 at 7:28
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    $\begingroup$ @JohnRennie : I think it is biophysics. Similar questions have been asked without being closed as off-topic. There is even a tag for it. $\endgroup$ – sammy gerbil Jun 29 '16 at 7:45
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    $\begingroup$ @tfb Who can answer this question? A medic? A mathematician? A chemist? A physicist? etc. If we had to choose one option, I think the best choice will be "physicist". $\endgroup$ – lucas Jun 29 '16 at 8:55
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    $\begingroup$ @lucas -- You are comparing the system efficiency of the human body to the ideal efficiency of an Otto cycle internal combustion engine. That is an apples to oranges comparison. The apple to apple comparisons are the ideal efficiency of a muscle cell to an ideal Otto cycle engine (the muscle cell wins), or the system efficiency of an exercising human to an automobile (the human wins). $\endgroup$ – David Hammen Jun 29 '16 at 11:20
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    $\begingroup$ Philosopher can answer this question: Can an Otto engine reproduce? I thought not. Go outside and find a tiny bug. It has sensory organs, a digestive system, can fly, learn, protect itself (like from weather or pursuit) and reproduce itself. Still think your iPhone is impressive? I think not. Give your Otto engine a few billion years to evolve, and then ask the question again. $\endgroup$ – user95006 Jun 29 '16 at 23:00

Can we compare alive cells with heat engines at all?

No, not really, because the living being isn't only a heat engine. There are three main points I want to make here.

1. Homeostasis Requires Constant Energy Input

This statement is especially true and obvious of homeotherms Mammals (Mammaliaformes, descended from the Therapsid Synapsid Amniotes), and Birds (Avialae / Dinosauria, descended from Dinosauriform Amniotes), which use a great deal of energy simply keeping their body temperature within strict limits, i.e. compensating for (mainly convective) heat loss from their body in cold conditions and actively expelling heat from their bodies in hot conditions. But, more generally, the phenomenon of homeostasis also requires expenditure of energy; a living organism is a highly non-equilibrium thermodynamic system, and excess entropies produced by metabolic processes must be expelled to keep it that way. Thermodynamic equilibrium is only reached when the living creature dies.

From this consideration alone, we would expect efficiencies measured when the organism does mechanical work to be considerably less than those of a heat engine.

2. Muscular Action is Not a Heat Engine

Muscular action is much more comparable to an electric motor than a heat engine. What I mean by this is an electric motor converts essentially work from one form to another with near to zero entropy change and negligible temperature change; motor proteins convert low-entropy energy stored as ATP to mechanical work through the hydrolysis of ATP with very small temperature change in the reagents as they react. In this case, the most meaningful measure of efficiency is probably expressed in two factors: (1) the ratio of the free energy $\Delta G$ of the ATP hydrolysis reaction to the total enthalpy change $\Delta H$ of the reaction (the difference $T\,\Delta S$ being the work we have to "give up" to expel the excess entropy of the reactants relative to lower entropy reaction products) and (2) the ratio of the mechanical work done to the available $\Delta G$.

In a heat engine, we take a quantity of heat from a hot reservoir, reducing the latter's entropy by $Q_i/T_i$ in the process, but find that, if we have a colder reservoir at $T_o<T_i$ we only have to "give back" $Q_o<Q_i$ to the cold reservoir to offset the entropy drop in the hot reservoir, so we get to "keep" energy $Q_i - Q_o > 0$ for doing work with. In biological reactions, the most comparable process to this is that of photosynthesis, where the "working fluid" of light at thermodynamic equilibrium at $6000{\rm K}$ is converted to "stored work" in sugars and, ultimately, ATP, dumping excess heat at ambient temperature $300{\rm K}$ in the process. Thenceforth, all living things use this low-entropy energy store rather like an electric motor converting energy stored in a capacitor, whether it be plants using it for their own life process, or herbivores accessing it through eaten plants or carnivores accessing it through eaten plant eaters.

So the plants and their solar energy fixing are the component of the biosphere most comparable to a heat engine in a power station; the plant metabolic processes and animals that eat plants and each other to get access to stored energy in plants are more like the electrical appliances that use the work extracted by the power plant, with very little temperature change.

3. Proteins Denature at Roughly $50{\rm C}$

For any animal process that could be considered to be like a heat engine, the maximum intake temperature can be at most a few or at most a few tens of degrees kelvin above ambient. This is because biological machinery is fatally damaged by temperatures much higher than $40{\rm C}$. Proteins denature and lose their vital life functions at very low temperatures. So if there are any processes in life that can be thought of as reasonably analogous to heat engines, we would foresee their efficiencies to be very low, since the theoretical efficiency is of the order of $3\%$ given this limit.

An interesting exception to my point 3 comes up in deep sea life living near hydrothermal vents. John Rennie writes:

Re the last point, the efficiency could of course still be 100% if animals had a heat sink at absolute zero. It's the fact there is a very limited temperature difference available that matters, rather than the limited source temperature. Note also that some extremophiles are quite happy living in near boiling water.

so we have creatures dwelling in $100{\rm C}$ and over environments and the opportunity to dump heat into the surrounding sea at much lower temperatures. However, my understanding is that these creatures still use the chemical energy from what they can extract from the volcanic vents, rather than working as heat engines taking advantage of the temperature drop.

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    $\begingroup$ Re the last point, the efficiency could of course still be 100% if animals had a heat sink at absolute zero. It's the fact there is a very limited temperature difference available that matters, rather than the limited source temperature. Note also that some extremophiles are quite happy living in near boiling water. $\endgroup$ – John Rennie Jun 29 '16 at 8:17
  • $\begingroup$ @JohnRennie See the update. Very valid point, but do you know whether these creatures actually use this much bigger temperature drop? My understanding was that the "producers" (plant analogues) were using what chemicals they can gather from the vents themselves, and then the others were eating them and each other. $\endgroup$ – Selene Routley Jun 29 '16 at 8:26
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    $\begingroup$ @WetSavannaAnimalakaRodVance: what I know about biochemistry you could tattoo on a flea's backside in a large font. However FWIW I don't know of any organisms using anything remotely like a heat engine (except arguably photosynthesis). The heat difference would have to be the temperature drop across the organism, so it's no use to an extremophilc bacterium that there's a 100C temperature drop available if only it was several metres in size. $\endgroup$ – John Rennie Jun 29 '16 at 8:32
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    $\begingroup$ @JohnRennie: Maybe I am misunderstanding your comment, but mammalian cells are not thermodynamic machines in the sense of combustion engines. The chemical energy is not converted to heat, first, before it is converted to chemical reactions or mechanical work. The more appropriate comparison would be with electrochemical cells. WetSavannaAnimal pointed out correctly that the overall thermodynamic efficiency starts with a 5800K temperature bath and it goes all the way down to the 2.7K of the CMB... that's what the entire ecosystem of Earth and its biosphere has to work with. $\endgroup$ – CuriousOne Jun 29 '16 at 8:37
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    $\begingroup$ So "old biophysicists don't die, they just reach thermodynamic equilibrium?" $\endgroup$ – Angew is no longer proud of SO Jun 30 '16 at 12:25

Why is the efficiency of human cells less than efficiency of an Otto engine?

It's not. You are comparing two very different things. The low value of 18 to 26% efficiency you found for the human body is the energy produced by an exercising human compared to the energy consumed by that person. The high value of 56 to 61% efficiency is for an ideal Otto cycle engine. You need to compare apples to apples.

Can we compare alive cells with heat engines at all?

In a sense, no, for the simple reason that cells are not heat engines. However, in the sense that thermal efficiency is the ratio of usable energy produced during a cycle to total energy (usable energy plus heat losses), one one can compute the ratio of usable energy produced during a muscle cell contraction / retraction cycle to the chemical energy consumed by that cell in performing that cycle. These efficiencies are comparable numbers.

There are plenty of published papers on this topic. For example, see Sharon Jubrias, et al., "Contraction coupling efficiency of human first dorsal interosseous muscle." The Journal of Physiology 586.7 (2008): 1993-2002, which finds that the muscles in a human hand are about 68% efficient. Also see Nathaniel's answer to the physics.SE question "Human as a heat engine".

The cells in a human body need to be quite efficient to obtain that apparently low value of 18% to 26% efficiency while exercising. There's a lot of energy consumption occurring in a human body in addition to the leg muscles used to power a bicycle. A certain amount if energy is needed just to keep every cell in the body alive. This includes the human brain, which consumes about 20% of this resting energy. The elevated energy consumption while exercising requires the heart to pump faster and your chest to breath faster. Those muscles are consuming extra energy while exercising but are contributing nothing to the work being performed.

Now let's look at an automobile. The 56 to 61% efficiency figure you cited is for an ideal Otto engine. The intake and power strokes in an ideal Otto cycle engine are adiabatic reversible processes. Those strokes are less than ideal in a real Otto engine reducing the efficiency considerably. An automobile has overhead costs, just as does the human body. Some of the energy produced by an automobile engine is used to create electricity and to power pumps and fans. Internal combustion engines lose yet more energy in the form of unburnt fuel in the exhaust, internal friction, and losses in the transmission.

The 18% to 26% efficiency figure is the system efficiency of a human body. When one looks at the system efficiency of an automobile, the ratio of the energy used to accelerate the car and push aside air to the energy consumed in the form of gasoline, it too is very low, in the single digits for city driving and low to mid teens for highway driving at non-excessive speeds.

  • $\begingroup$ May you please compare ideal efficiency of human (or muscle cell) with the efficiency of a Carnot cycle, too? Thank you again! $\endgroup$ – lucas Jun 29 '16 at 11:55
  • $\begingroup$ @lucas That's pretty hard to compare. For example, the main power source of a human cell is ATP-synthase, which is basically an electric motor - converting an electro-chemical potential to chemical intermediate storage, ATP. This ATP is then used to relax the muscle cell. This part is extremely efficient, similar to macroscopic electric motors. On input, you need the electro-chemical potential, usually supplied by a complex machinery that breaks down sugars. This is trickier - it depends on temperature, and releases significant waste heat. For humans, it seems to have ~40% efficiency. $\endgroup$ – Luaan Jun 29 '16 at 14:35
  • $\begingroup$ @lucas That's where you really feel the low temperature of the processes occuring. If our body temperature was higher, sugar->potential would be much more efficient. However, it would also require higher expenditure to keep the body at that temperature (assuming we would still live in the same conditions), which would negate all the benefit. Don't forget that the waste is usually still quite useful in keeping our (necessary) stable temperature. It's kind of like incandescent light bulb - working double shift in winter, where all the "waste" heat is utilized, wasting energy in summer. $\endgroup$ – Luaan Jun 29 '16 at 14:41
  • $\begingroup$ @Luaan Thank you because of your attention! I didn’t mean to compare numerically. I wanted to know if there is any irreversibility inside the cells. If so, we can say that cells efficiency is less than Carnot efficiency. $\endgroup$ – lucas Jun 29 '16 at 15:55
  • $\begingroup$ People are much more efficient running on the highway than in the city. Wait... $\endgroup$ – user95006 Jun 29 '16 at 23:03

Let's calculate engine efficiency by using the ratio of work and gasoline energy (assuming it can be completely converted to CO2 and H2O). And let's calculate cell (muscular) efficiency by the ratio of work (from gym equipment) and fat energy (assuming it can be completed converted to CO2 and H2O). These two efficiency are comparable.

A gasoline engine efficiency is about 30%. If the oil processing is included, it can be even lower. Cell efficiency 18-26% is not too low. The question might be where does the rest 82%-74% energy go? My thinking it can be used to accelerating circulation system (increase heart beating frequency, transporting material like oxygen etc) and it is used up as heat is removed from the body. A demographic plot should be a study topic for bio engineering scientists.


First. Carnot engine is the ideal heat engine. It is already highest efficiency possible for its kind

Second. Efficiency need high maintenance cost. You need specific material, specific fuel, specific condition to work and most important it could do only specific task. To make something just work and durable and reuse what it already there is better to survive in nature

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    $\begingroup$ I don't see how this answers the question. $\endgroup$ – John Rennie Jun 29 '16 at 7:30
  • $\begingroup$ @JohnRennie To put it simply. Evolution of animal cell just use any cycle with enough efficiency to have lower maintenance than high efficient $\endgroup$ – Thaina Jun 29 '16 at 7:33
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    $\begingroup$ Lucas asks; Is there any explanation for this? Which cycle do human cells work with? Can we compare alive cells with heat engines at all?. All you've given are some general statements that cell efficiency is lower than the ideal efficiency. No specifics at all. $\endgroup$ – John Rennie Jun 29 '16 at 7:38

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