# Can Thermal Energy be converted into usable energy?

I'm going to go out on a limb and ask a question that will probably be a bit humiliating: Can Thermal Energy be converted into usable energy? I've been reading about conservation of energy, and I know that in no conversion is all the energy usable. There is always some thermal energy (which leads to the conclusion of the inevitable heat death of the universe). But couldn't this problem be avoided by turning the thermal energy into forms of usable energy?

Nothing I've read ever said that thermal energy couldn't be changed back, so why don't we do it? Is it impossible? (Which I find hard to believe). Is it too inefficient? (That would mean that the thermal energy is converted into, well, more thermal energy. Which we can make more usable energy out of. Still more inefficiency? Do it again.) Is there some other reason? Or is there an actual theoretical way to turn thermal energy into usable forms of energy?

To turn thermal energy into useful work completely one would need a thermal bath at the temperature of absolute zero. This is explicitly forbidden by the third law of thermodynamics. The best one can do is given by the efficiency of the (theoretical) Carnot cycle: http://en.wikipedia.org/wiki/Carnot_cycle. Th efficiency of the Carnot cycle only depends on the ratio of the temperatures of the cold and the hot thermal baths that a cyclical thermodynamic machine has access to:

$\eta= 1 - T_{cold}/T_{hot}$.

As you can see from the formula, if $T_{cold}=0$, then the efficiency would be equal to one, i.e. all thermal energy would be converted. That, as we said, is forbidden, because of $T_{cold}>0$. On the other hand, if $T_{cold} =T_{hot}$, then the efficiency of any thermal machine is zero, i.e. one can't extract any useful energy from just one temperature bath.

Practical efficiencies that can be reached with real thermal machines range up to 60% (in combined cycle natural gas plants, I believe), but it becomes increasingly more expensive to improve efficiencies, so at some point the cost of the improvement is higher than the cost of the lost energy, at which point economics sets a limit to energy efficiency. A better way to use the lost heat is for heating purposes. Combining a small power plant with the heating systems of buildings makes almost 100% use of the energy in the fuels that are being burned in the power plant. These cogeneration facilities (named so because they produce electricity and useful heat) are playing an increasingly larger role in energy efficiency improvements.

• Even still, there is an incredible amount of thermal energy in the universe. You've shown that it is possible, theoretically, to convert almost all the heat in a temperature bath. Then add more heat. If we're using the energy, it'll become more heat to use. You could then say that that little bit of heat energy left each time will accumulate for the eventual heat death. Okay, if it's accumulating, just use it once it becomes enough. So could we theoretically prevent the heat death of the universe as long as we existed to do so? Oct 15, 2014 at 19:56
• Posted that before your edit. But reaching maximum cost-effective efficiency, couldn't we make enough to achieve the same effect as I mentioned? Oct 15, 2014 at 19:58
• The limit is the cold temperature bath. The coldest temperature bath in the universe that exists in virtually "unlimited" quantity is the cosmic microwave radiation, so that's 2.7K, very close to absolute zero. The problem with that is that a radiator at 2.7K is extremely inefficient, so we can't practically make use of that particular thermal bath. On Earth it's technically hard to heat machines higher than to approx. 1200K degrees and to have the cold bath lower than maybe 400K. Real machines will always be less efficient than the Carnot limit... so that's the technical limitation to 60%. Oct 15, 2014 at 19:59
• For theoretical purposes one could add that black holes should have temperatures that are extremely close to 0K, so, at least in theory, a thermodynamic machine converting heat using a black hole as a heat dump should have an efficiency of almost 100%. I do not know if the naive thermodynamic limit is correct for black holes, though. Oct 15, 2014 at 20:07
• Say we placed our observations on just one solar system, and took the unusable thermal energy we produced and converted into as much usable energy as we could, which we use, making excess thermal energy again, although not as much as before. Since there isn't as much as before, obviously the trimmed thermal energy is outside of the system in question. So we take back the thermal energy that had escaped, although not necessarily the same thermal energy, just the same amount, and then the original quantity of energy is back in the system. Oct 15, 2014 at 20:09

It is possible up to the Carnot limit, which is never 100%. In particular, the Carnot limit is higher if the temperature before extracting is higher. But you could only hit 100% if the temperature could reach infinity, which it can't.

There was a time, when trains worked on coal. What sort of energy, do you think, it was? - Thermal.

There's also solar energy, which is, if you think thoroughly, thermal energy. You turn heat (received by a solar panel) into an usable energy source. However, as I know, solar energy produces so little electricity, it's not worth all the effort.

The way, I see it: if that massive heat energy source (the sun) can't produce energy enough to use it efficiently (I mean, if you don't have extremely large solar panels*), what other sources do you recommend?

*There are projects somewhere across the globe, when people cover their whole roofs with solar panels and yet they produce about 10% of the energy needed for that house.

• Actually, no, they didn't run on thermal energy. The steps: Coal was burned, which was converted into steam, and the steam turned turbines which ran the train. Solar energy is called Radiant Energy, which is converted into Electromagnetic Energy by the cells. The thermal energy is that which is released by the inefficiency, and it's not usable for electricity at all without converting it. Oct 15, 2014 at 19:54
• Well, my apologies... Oct 15, 2014 at 19:55
• Oh, it's no problem. Thank you for putting thought into helping me answer the question! Every raised concern helps to increase the thoroughness. Oct 15, 2014 at 20:00

Thermal energy can convert directly to usable electricity via a thermionic energy convertor (TEC). Heat excites electrons at the surface of a metal, which electrons escape the metal surface (typically a filament) and become free-electrons (Edison Effect). Using vacuum electronics or vacuum semiconductors, these free electrons can form electron beams and power Inductive Output Tubes (IOT), magnetrons, particle amplifiers such as klystrons, and TECs. In the latter case, capturing the electron beam results in capturing the converted energy. Patented in 1915, used by Soviets in spacecraft in the 1960s, low conversion efficiencies (<10%) have militated against commercialization. Recent prototypes at Max Planck Institute and at Space Charge LLC now target conversion efficiencies of 50%.

Only thermal gradients can be turned into usable energy. There's a general principle that gradients of physical quantities can be used to drive processes. Take a look at this table$$^\dagger$$ I took from my lecture notes The quantities in the leftmost column are things that can be transported (mass, heat etc.) and the quantities in the top row represent energy gradients that can drive transport. Each entry of this table will generate a transport law of the form $$J_i=L_{ij}\nabla X_j.$$ Along the diagonal we have for example Fick's diffusion law, which is about transporting mass. Fick's law is given by $$J_\phi=-D\nabla \phi$$ with $$\phi$$ the concentration. Also Ohm's law, which is about transporting electrical energy, becomes $$J_E=-\sigma\nabla V_E$$ with $$V_E$$ the electric potential such that $$E=-\nabla V_E$$.

The interesting effects occur at the off-diagonal terms. The Peltier effect for example can use electricity to provide cooling (or heating). An interesting result that follows from the second law of thermodynamics is that $$L_{ij}$$ is symmetric, i.e. $$L_{ij}=L_{ji}$$. In practice this means that for any of these off-diagonal processes there's some reverse process. If we look at the partner of the Peltier effect we find the Seebeck effect which uses thermal gradients to generate a voltage. So it is essentially the reverse.

$$\dagger$$ These lecture notes are sadly not publicly available.