Eli5: Why cant we use boyle’s law to extract energy from hot air

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Things i know:
1. boyle’s law vaguely as; as pressure rises so does temperature.

2.Peltier devices can extract electricity given a large enough temperature differential, are there devices that do this better?

3. Heat pumps can pull heat from cold air on one side and make hot air on the other side.

I know i am missing some major steps here and ifs something ive always wondered about…

In: Physics
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The problem is, the amount of energy you would get from extracting the energy from the hot air would be less than it would take to run the heat pump to generate the hot air. Heat pumps use a ton of power to operate.

I’m a bit confused where boyle’s law comes in here.

Yes you could use a heat pump to create a temperature gradient that could power a peltier (thermoelectric generator in this use case) but as neither of those thing are perfectly efficient the energy given from the peltier is less than the energy used by the heat pump.

It’s fundamental impossible to get all the energy technically available from a temperature gradient.

What you’re thinking of is a thermoelectrical generator, or a Seebeck generator, which is the reverse of a Peltier device. The Seebeck generatore creates electrical current from a temperature difference, while a Peltier device generates a temperature difference given an electrical current.

The problem is one of efficiency. A thermoelectric generator is very inefficient (<10%). This means that it generates a lot of heat and/or bleeds a lot of heat from the hot side to the cold side for the amount of power generated. So you wouldn’t be able to pump all the heat back (returning the system to its original state) using just a heat pump and the energy you got from the thermoelectric generator.

Boyle’s Law isn’t directly related to temperature; instead, Boyle’s Law simply states that changes in volume are inversely proportional to changes in pressure. In most applications, though, compressing a gas isn’t an isothermal process; pressure changes are typically accompanied with temperature changes.

As far as what you’re talking about; the primary limitation is the 2nd law of thermodynamics. ***All*** heat engines are limited by Carnot’s Law, which essentially states that your maximum efficiency is directly tied to the difference in temperatures across your reaction. In essence, the lower your temperature differential between the heat source and the ambient, the less efficient the process will become. As a direct result, most low-temperature heat engines have absolutely garbage thermal efficiency, and thus past a certain point there really isn’t much reason to use a heat engine.

I think you mean “pressure law” for the P1/T1=P2/T2 equation. And I mean, yes an engine that uses heat to create pressure and kinetic force exists, check out Stirling engines. You basically heat up one end of the cylinder and cool the other end with a moving valve/rod in the middle to harvest kinetic energy off the repeated expansion and compression of fluids based on changing temperatures as you manipulate the position of liquids. They’re actually more energy efficient compared to combustion engines so some people consider them as the future, but as for now they just simply don’t generate enough force to be considered useful.

You could, in theory, but you’d have to put more energy into the heat pump than you’d get out of it.

I can’t juggle the equations in my head but either you’d always get less energy out of it than you were putting in, or one side of it would have to get hotter and hotter and hotter forever. I think it’s the first one.