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If one could devise an answer to this question, electricity would be free for everyones disposal. (seems like a good dream but in reality free energy will be this worlds downfall)

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closed as not a real question by David Z Feb 2 '13 at 5:07


Hi 925, and welcome to Physics Stack Exchange! Could you clarify what you mean by extracting and concentrating heat? (The answer will be "no" pretty much regardless of what you do mean, but it's best if your question is detailed enough that we can give it a proper explanation.) – David Z Jan 12 '12 at 7:41
This question fails to make any sense when read in full. – Nic Jan 12 '12 at 11:21

Yes, heat can be extracted and concentrated: that's exactly what a heat pump does. For example, let's consider an air-source heat pump operating at an ambient air temperature of 270 Kelvin. The heat pump will cool some of that air down to say 260 Kelvin; and concentrate that heat into a much smaller volume of air, heating it up from 270 Kelvin to say 300 Kelvin.

No, you cannot do this to get net work done: this cannot give you free electricity, because it takes work to extract and concentrate heat, and the second law of thermodynamics means that it will always take you more work to extract and concentrate the heat, than you could get out of the concentrated heat.

The principles behind the limits on concentrating heat, and on getting work from heat, were first set out by Sadi Carnot, and the limits are named after him.

For a heat engine, the most work you can get from it is given (all temperatures in Kelvin) by: $$\frac{T_{Hot}}{T_{Hot}-T_{Cold}}$$

For a heat pump, the maximum coefficient of performance [COP] (the amount of heat out, for a given amount of work put in, is


So in our example of a heat pump raising the air from 270 Kelvin to 300 Kelvin, the maximum COP is given by: $$\frac{300}{300-270}=10$$ but in the real world, you're more likely to see a COP of about 5 under those conditions (i.e. about half the Carnot limit). That is to say, for every 1kWh of electricity you put into the heat pump, you'd get 5kWh of concentrated (at 300 Kelvin) heat out.

If you then wanted to create a heat engine by cooling that 300 Kelvin air back down to the ambient air temperature of 270 Kelvin, the best efficiency you could manage would be given by:

$$\frac{300-270}{300}=0.1=10\%$$ Again, real-world heat engines don't reach the Carnot limit, but you might get 50% of the Carnot limit, i.e. 5% of the thermal energy would get turned into work.

So your round-trip efficiency from concentrating the heat, then doing the work, would be given by COP multiplied by the heat-engine efficiency, i.e. 5x5% = 25%. This is equivalent to the product of the two Carnot efficiencies: the heat pump has a Carnot efficiency of 50% (i.e. it's operating at half the Carnot limit); and the heat engine also has a Carnot efficiency of 50%; and that product is 25%

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One can't extract and concentrate heat because of the so-called "second law of thermodynamics", a law that expresses irreversibility of macroscopic phenomena in Nature. It's a law that says that the machine you are proposing as a source of energy, the so-called "perpetuum mobile of the second kind", is impossible in Nature. (The "perpetuum mobile of the first kind" violates the energy conservation law, i.e. the first law of thermodynamics, outright, and is also impossible.)

Such a device would be able to take the energy from an object by cooling it, and use this energy for useful purposes e.g. for mechanical energy to lift an elevator. Indeed, as you correctly stated, this would need energy to be "concentrated" because when it's in the form of heat, the energy is distributed among all the atoms and molecules.

But energy can't be concentrated because that would mean that at some point, we have to move the heat from a colder object to a warmer object. However, because the "entropy" has to go up (another way of stating the second law of thermodynamics), the heat always flows from a warmer object to a cooler one, thus making the temperature profile more uniform (not less uniform) as time goes by. In this sense, the heat is always getting "less concentrated" and more diluted all over the physical system.

The heat that is already contained in an object at thermal equilibrium – with a fixed temperature everywhere – cannot be "extracted" because it is not a "useful form of energy". The only heat that may be "extracted" and converted to a useful form of energy, e.g. the mechanical one, is the heat stored in temperature differences between different objects or their part. This heat is the energy waiting to be transferred from one place to another which is what can do work.

To make the terminology confusing, the amount (subset) of energy of a system that is capable of doing work is known as free energy

in physics. Of course, the adjective "free" has nothing to do with the price in dollars or with applications for the mankind. One must warn against this confusion because both meanings of "free energy" – the physics concept of energy that is freely floating and waiting to be usefully employed; and energy that may be promised to everyone free of charge (and these economic and policymaking concerns and pledges have pretty much nothing to do with physics) – appear in this single discussion.

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while this question correctly answers the questioner's intent, I feel that the opposite statement (if not meaning) is also true, cf. EnrgyNumbers' answer. – Nic Jan 12 '12 at 11:23

Using a heat pump we can extract plenty of low grade heat. At this point everyone always talks about converting the heat into some other form of energy. We need to make the heat work for us directly. I like the idea of using a heat pump to cool a black panel as a solar collector. The output would be very good but after your house warms up what's next? This is not a dead end but we really do need to put our heads together and ask "what can we do with all this heat?" There is an answer out there.

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Welcome, Ryan. Just remind that it is not a forum. When you answer the question, please write things more related to the question, not a general disscusion. – hwlau Feb 2 '13 at 3:35
