# Why is it so inefficient to generate electricity by absorbing heat?

When I turn on a heater, it's supposed to be roughly 100% efficient. So it converts electricity to heat with great efficiency, but why can't we do the reverse: generate electricity by absorbing heat? I have been searching the internet and from what I have read it seems completely pointless because it is so inefficient, like ridiculously inefficient, as in 10% efficient. So why can't we do the reverse? I get that energy is lost when converting from one form of energy to another but how can we get such great efficiency going from one form but have horrid efficiency going back?

I also read online that one way to cool the earth down could be to radiate the heat off the planet. Anyways, sorry about my mini debate, can anyone answer how we could potentially cool the earth, because to me it would seem funny if we couldn't, and if we could then global warming wouldn't be as bad of a thing as it is now, would it?

• Also note that a machine that converts heat into electricity is really converting a temperature difference into electricity. If you have a warm thing and a cold thing next to one another, they tend to want to equalize, and you can get in on that action and get some electricity (or other energy) out of it. But once the temperatures are equal, your machine won't work any more. There is no machine that you can put in the middle of a warm room that will make the room colder and give you electricity (as long as the machine has the same temperature as the room). Jan 8, 2018 at 16:38
• When I let go of a rock, it falls to the ground with 100% efficiency. Why do rocks not spontaneously hop in to the air? Why are they so bad at doing that?
– user169874
Jan 8, 2018 at 17:10
• You have a box with 1,000 chickens in it. Want them to spread out, just open the box. Want them back in the box? It's not so simple. Jan 8, 2018 at 22:44
• "like ridiculously inefficient, as in 10% efficient" ever thought about the efficiency of incandescent bulbs? Jan 9, 2018 at 14:57
• @PlasmaHH Incandescent lightbulbs are nearly 100% efficient... if your goal is to heat the room. :) Jan 10, 2018 at 3:07

"So, why can't we do the reverse?" Because of the Second Law of Thermodynamics! Very, very roughly, heat is 'thinly spread' energy and won't spontaneously organize itself into the 'concentrated' energy that we want (in the same way that a drop of ink released into a tank of water won't spontaneously gather itself up into a drop again). Advice: if you're really interested, read up about thermodynamics!

• Comments are not for extended discussion; this conversation has been moved to chat.
– rob
Jan 9, 2018 at 5:21

tl;dr- Current technology absorbs temperature gradients, not heat. As temperature gradients become arbitrarily large, their information content nearly approaches the heat's information content, such that the apparent thermal efficiency,$${\eta}_{\text{Carnot~efficiency}}~~{\equiv}~~\frac{E_{\text{useful}}}{E_{\text{heat}}}~~{\approx}~~1-\frac{T_{\text{cold}}}{T_{\text{hot}}} \,,$$nearly approaches unity, showing that we can almost absorb heat while a temperature gradient is sufficiently large.

### Hypothetical/future technology: Absorbing heat for energy

You could harness heat with near-perfect efficiency! Just requires finding Maxwell's demon. Maxwell's demon can be tough to find, but Laplace's demon could tell ya where it's at.

The fun thing about Maxwell's demon is that it likes to separate stuff out based on its highly precise perception and movement:

.

So, you basically tell Maxwell's demon to let out high-speed particles when they're at nearly-tangential velocities to power a dynamo. And, bam! Electricity.

One trouble with this scheme is that we don't really know what heat is. I mean, we get the gist that particles are bouncing around and such, but we don't know all of the exact locations and velocities and such for all of the particles. And given that ignorance, we're basically unable to do anything with heat.

Except, of course, when our ignorance isn't complete. At the macroscopic level, we can appreciate stuff like temperature gradients; the larger the temperature gradient, the more information we have about relative motion of the particles at different temperatures.

And we can exploit this information, up to the point at which we've drained it away. For example, we can use heat to boil water, producing steam and thus raising pressure, using that pressure to turn a turbine. As the steam turns the turbine by going from a region of higher pressure to lower pressure, we again lose discriminating information about the system until our ignorance is again complete; but, we get useful energy out of the deal.

Conceptually, it's all about information. Whenever we have information about something, we may be able to turn that information into effect until the point at which we cease having information. Though we might say that we don't necessarily lose all of the information, as the energy that we get out of the deal isn't so much actually "energy" quite so much as it's a system that we have relatively more information about, and thus can exploit more readily.

Maxwell's demon and Laplace's demon are powerful critters because they have tons of information. By always having information, they can always construct systems that they can exploit for the extraction of energy. By contrast, humans tend to be limited in what information we have.

And that's the problem with just arbitrarily absorbing "heat": heat is a vague description about stuff moving around. In fact, even knowing a temperature is fairly useless information by itself; rather, we need temperature gradients, i.e. discriminating information, to knowingly construct a system that behaves how we want it to, e.g. a power generator.

In real life, there's interest in creating molecular machines, like observed in the classical example of ATP synthase, as a future technology. As @J... pointed out, Maxwell's demon in the above is acting as a thermal rectifier which are currently being researched (example).

### Current technology: Absorbing temperature gradients, not heat

Why is it so inefficient to generate electricity by absorbing heat?

The above describes a system for generating electricity from heat. However, current technology never does this.

With current technology, we absorb temperature gradients. This may sound pedantic, but the fact that we're absorbing gradients and not heat itself is precisely why we can't get the energy equal to the heat out of the process.

Since we absorb the gradients, the Carnot efficiency tends to increase with the size of the gradient,$${\eta}_{\text{Carnot~efficiency}}~~{\approx}~~1-\frac{T_{\text{cold}}}{T_{\text{hot}}}.$$

Conceptually, the reason for this is that, as the temperature gradient$${\Delta}T~~{\equiv}~~T_{\text{hot}}-T_{\text{cold}}$$becomes arbitrarily large, the information contained in knowing the temperature gradient approaches the information that Laplace's demon would know, at which point efficiency would approach unity:$$\lim_{{\Delta}T{\rightarrow}\infty}{\left(1-\frac{T_{\text{cold}}}{T_{\text{cold}}+{\Delta}T}\right)}~~{\rightarrow}~~1,$$i.e. 100% efficiency.

This is, sure, you wouldn't know the exact velocities of all of the particles, but what you don't know is dwarfed by what you do know, i.e. the extreme relative temperature gradient.

• Comments are not for extended discussion; this conversation has been moved to chat. Jan 9, 2018 at 18:43
• This answer's irking me a bit because I tried to talk about interesting aspects of the theory, but in the process, I ended up simplifying a lot, omitting points, not explaining basic background principles, hacked the notation a bit, etc.. If anyone'd like to suggest little tweaks or improvements, such suggestions would be entirely welcome!
– Nat
Jan 9, 2018 at 20:40
• @Nat To expand on the hypothetical technological use, is suspected that while Maxell's Demon may be possible, it would end up consuming more energy itself than you could produce by using the separation.
– Eth
Jan 10, 2018 at 11:13

When you use heat to produce electricity (or any other form of energy), you are limited by Carnot efficiency:

$$\eta = 1 - \frac{T_C}{T_H}$$

You cannot produce any useful work using a heat source alone - you also need a cold environment to absorb the heat in the process. This is why it's pretty much impossible to make everything in the world simultaneously cooler when using a heat engine, and why it's impossible to achieve 100% (or even near-100% efficiency) with it, unless you're ready to go to a planet with near-absolute-zero ambient temperature.

I get that energy is lost when converting from one form of energy to another but how can we get such great efficiency going from one form but have horrid efficiency going back?

Energy is never lost, or created out of nowhere. Colloquially, "energy is lost" means that some of it got converted to heat instead of the form you wanted. This is why a heater is said to have 100% efficiency.

• There is not even any such thing as a heat source, in the absence of a "cold source". Jan 8, 2018 at 17:59
• This seems like a great (and very precise) explanation of what the limit is, but does nothing to answer the original question about why the limit exists. Jan 8, 2018 at 21:07
• @DanielWagner because you carnot do any better than that, so everything else is less efficient.
– user169874
Jan 9, 2018 at 2:05
• @DanielWagner I don't think there is a logical answer to why the laws of physics are the way they are. Jan 9, 2018 at 7:44
• @DanielWagner No, physics never really answers the question "Why?". Just how. Even if you go to the next level down its still just answering a more detailed how. Weather or not you can use a lower level understanding to make a meaningful why in your logic framework, its still not fundamentally answering why. Now i agree that this is not a very good answer and indeed many thermodynamics effects are very simple on a fundamental level. In essence they are just random processes and millions of simple rules. However the end results are highly emergent, that is not self evident from the rules. Jan 9, 2018 at 10:14

## Image

"Why" is generally a difficult question to answer. But in this case it is really easy to draw a mental picture:

Imagine a complete set of billiard balls nicely ordered in their usual triangle formation. As a analogy, this corresponds to something that is comparatively cold, (i.e., the atoms wiggle around relatively little and are more ordered when colder - of course, colder atoms are not standing still like the billiard balls).

Now the game starts, and a good player hits the balls so they are spread out over the whole table. This corresponds to the higher entropy of a warmer situation, (i.e. the disorder of the warmer, more wiggling atoms increases).

Note that it does not matter how the balls come to rest: any configuration of the balls is widely different from the original starting triangle - this disorder corresponds to a higher entropy state. There is only one low entropy, highly ordered starting position, and many high entropy, disordered states after the breaking the triangle. It is very easy to create any chaotic configuration of the balls (just hit them with the cue however you like). It is quite unlikely to produce an ordered state, like the triangle configuration, (which corresponds to ordered, coherent, useful energy). Collision with the cue is very unlikely to return them to the triangle frame (i.e. it is unlikely for atoms randomly colliding with each other to all move in the same direction).

Now, to relate to your question:

• The balls are the atoms.
• Balls in an ordered state (triangle) correspond to colder atoms.
• Balls in a chaotic state correspond to warmer atoms.
• Electrons correspond to the cue ball (in a wire with current flowing in it).

Orderly electrons (currents) randomly hitting atoms easily make the atoms they hit in a wire wiggle around more (heat them up), which means it is easy to build an electric heater.

The reverse, heated atoms causing electrons to move in an ordered fashion, will not happen spontaneously because it is an extremely unlikely possibility. Therefore, we cannot depend on an "accidental" current being generated from heat.

We can and it is already done. You have thermoelectric generators - basically a Peltier element as you use to cool CPU in personal computers (but put in reverse). You make one side hot and the other cool and you get an electric current. How do you make the heat? Well that's up to you. You can try by optics or heating water (like "backwards water cooling", lol). There are lots of people experimenting on youtube if you want to learn some about it.

How do you get the cool then? Well outside the ground is often cool. Water is a good coolant et.c.

• Peltier elements are not usually used for cooling CPUs. Yes, such coolers exist on the overclocking enthusiast market, but it's actually a quite wasteful practice because the Peltier elements are very inefficient indeed (as the question correctly premises, and your answer seems to contradict) and have to work against the flow. That cooling energy would better invested in powering another regular-fan-cooled processor, or an whole array of passively-cooled e.g. ARMs. Jan 9, 2018 at 0:03
• Peltier elements are lame for CPU cooling, I have tried it and the results are they use way to much power for the amount of cooling you get. You can achieve much better results with water cooling like a cosair h80i or similar. Jan 9, 2018 at 0:22
• @cybernard you have tried it and you don't know you can couple the peltier element with a water cooler..? Jan 9, 2018 at 7:37
• @mathreadler Yes, I tried it with a water cooler, and the temperature advantage vs power draw and it just wasn't worth it. The water cooling kit alone was the best bang per watt. Jan 9, 2018 at 12:37
• These do not generate electricity (like this question asks), but just shift heat energy around from one place to another. They require energy input.
– AnoE
Jan 9, 2018 at 14:48

Your first question is answered by the following:

When you turn on a heater, Joule effect is at work to convert the electric energy into heat. This effect is irreversible. What is meant by that is that if you could film a movie of the heater and run that movie backward, the laws of Physics would not hold anymore. Indeed, you would see that the current gets its direction reversed and you would see the heater cooling itself. However the Joule effect behaves as $\sim I^2$ and so changing $I$ by $-I$ does not change the Joule effect and you would expect the wire not to be cooler if the laws of Physics held (more precisely, Ohm's law).

Now answering the "why is it so inefficient to convert heat into electricity?":

First of all, devices that convert a temperature difference into a voltage are called thermoelectric generators (TEGs). Their principle of functioning is based on the reversible Seebeck effect. The main answer to your question is not that these engines are indeed limited by Carnot's efficiency as stated by others here (because they are heat engines, which is true), but because we have not yet found materials good enough to ensure a higher efficiency. If the former reason held true, then there would be no point in trying to improve the efficiency of current TEGs, while in reality it is currently a hot topic in materials science (and has been in the last century too, with ups and downs). Thus, some scientists have hopes that one day we will find materials good enough to make TEGs competitive with other green energies such as solar energy. Note that the efficiency of a TEG depends on the temperature difference. It does not make much sense to quote a "10%" efficiency without specifying the temperature difference. For a few degrees Celsius as $\Delta T$, the efficiency is closer to 1% than to 10%.

Having this in mind, a useful parameter related to the thermoelectric efficiency of a material, called the figure of merit or $ZT$, which is equal to $\frac{\sigma S^2}{\kappa}$, where $\kappa$ is the thermal conductivity, $\sigma$ is the electric conductivity, and T is the absolute temperature, gives us some clues on which properties a candidate material for TEG has to satisfy. Roughly, the material needs to have a high Seebeck coefficient, a low thermal conductivity and a high electric conductivity. In many metals, the Wiedemann-Franz law holds and stipulates that good electric conductors are also good thermal conductors and so they are not good candidates for TEG materials. Nowadays TEGs are made with n-type and p-type semi conductors elements. In today's research, scientists have found ways to improve the ZT factor to around 2 by shaping materials at the nano scale (See this ref for instance.). The topic is very broad and deep.

I will not answer the last question about Earth cooling down because it's too unrelated to the first questions and might deserve to be posted in a new question if it hasn't already been posted.