# Heat engine efficiency curse [closed]

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.

• Comments are not for extended discussion; this conversation has been moved to chat. Aug 7 at 22:36

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.