Let's consider a brick. Usual building brick.

Further, let us set up two "brick-engine/storage".

Gravitational brick-storage Thermal brick-storage
0. Let's measure how effectively the brick transforms PE (potential energy) into W (work) a. Let's measure how effectively the brick transforms TE (thermal energy) into W (work)
1. Let's raise the brick to height $h_1$ which takes us 200J of work b. Let's work on the brick to heat it up to $T_1$ (bore into it or something), the boring takes us 200J of work
2. Let's drop the brick from $h_1$ to $h_0$ c. Let's let the brick cool to something close to $T_0$
3. When the brick hits the ground scale or some device* we get our 200J back in the from of work (see *), right? d. When the brick cools, we DON'T get 200J back in the form of work no matter what.
So it seems that vanishing gradient of $\Delta h$ (the falling) does not affect the gravitational engine's efficiency, right? The vanishing gradient of $\Delta T$ (the cooling) does affect the thermal engine's efficiency.

*This ground device is capable of transforming KE into work with 100% efficiency, so that all is left for us is to consider whether the brick was able to convert its PE into work with 100% efficiency or not.

Now the questions:

  1. The efficiency of the heat engine is a function of $\Delta T$, but the efficiency of the gravitational engine is NOT a function of $\Delta h$, right?
  2. Is heat engine unique in this regard? It's unlucky since the thing which powers it (the $\Delta T$) is the same thing which hinders it (since when the engine cools, the $\Delta T$ is getting smaller and the efficiency of the engine drops).
  3. Are there other "engines" working between other gradients like pressure, voltage, etc., in which efficiency is likewise cursed? The curse being: gradient vanishes and efficiency drops
  4. Is there a table or a list of all the efficiency formulas somewhere for different types of engines so that I could see whether the "heat engine" is uniquely cursed or not.?

P.S. I sence that there are many holes in the table above. Please, If you see them, make your own version of the given table and the exmaples above (the gradient of height and temperature). Clarifying your version of the above examples, might give me additional food for thoughts. My mind is in flux and I can't formulate the questions and the table better. Help, if you can. Thanks.

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Aug 7 at 22:36

The difference between your two processes is that the left hand column is a reversible process - or, at least, it can be made reversible as long as we use the falling brick to do work without letting its temperature change and without letting energy escape into the environment as, for example, sound waves. The right hand column is an irreversible process. Another way of saying this is that the brick in the left hand column is always in thermal equilibrium with its environment, whereas the brick in the right hand column is not in thermal equilibrium because it is being heated up and cooled down.

All of the energy stored in a reversible process can, in principle, be recovered as work. So an engine based on a reversible process can have an efficiency of $100\%$. But some of the energy stored in an irreversible process is lost as heat energy and cannot be recovered as work. So an engine based on an irreversible process can never be $100\%$ efficient.

Note that a reversible process is a theoretical idealisation. All processes in the real world are irreversible to some extent, although we can make then close to the reversible ideal if we take care to minimise friction, vibration and temperature changes.

  • $\begingroup$ So friction, temperature change, and vibration are key to entropy. Anything else? And irreversible is THE key? Why vibration? $\endgroup$
    – Al Brown
    Aug 5 at 13:55
  • 2
    $\begingroup$ Re "reversible" vs. irreversible: The gravity brick stores potential energy, and the laws that describe it allow you to treat it as a single particle. The hot brick, on the other hand, stores energy as the kinetic energy of all of the multitude of molecules that comprise it. The number of possible states for the hot brick is inconceivably huge. The only way to describe it is with the statistical laws of thermodynamics. You could, in in principle, reverse the process; but only if you could instantaneously, and precisely reverse the path of every atom in the entire system. $\endgroup$ Aug 5 at 14:20
  • $\begingroup$ @SolomonSlow I think that deserves an answer; it would be an even better one if you can illustrate how entropy emerges from the statistics (which I can't see myself) $\endgroup$ Aug 5 at 21:51
  • $\begingroup$ @SolomonSlow You are correct. “Irreversible” processes can, in principle, be reversed. But it is practically impossible to reverse them intentionally, and massively improbable that they will reverse spontaneously (whereas the raised brick will fall down again if not supported). But “irreversible” is standard terminology. $\endgroup$
    – gandalf61
    Aug 6 at 6:49

Entropy is the key here. The heat engine is the only engine type that withdraws entropy (because the heat engine relies on a temperature difference; since entropy is the conjugate thermodynamic variable to temperature, entropy shifts when things cool down). But the work you obtain carries no entropy, and entropy can’t be destroyed. Thus, you must waste some of the available energy to dump the entropy elsewhere. Other engine types don’t encounter this problem because they rely on nonthermal gradients.


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