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Comment by contravariant | Hacker News Reader

It's not that heat pumps aren't capable of making a 1000K temperature difference, but with an ambient temperature of around 300K even the theoretical advantage of using a heat pump instead of straight up heating is just ~40%.

It's not nothing, but getting close to the theoretical limit tends to be incredibly annoying when it comes to thermodynamics. Typically it requires doing stuff extremely slowly (so you're always close to thermal equilibrium), which means it's nowhere near fast enough or you need almost perfect insulation etc.

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Why is the ambient temperature important? Isn't it about thermal energy? So wouldn't a heat pump just need to be much larger to work up to 1000 degrees or more?

Say, I have a heatpump that heats up water to 100°C at ambient temperature of 10°C. Couldn't I feed that hot water into another heat pump that heats up water to 200°C and so on?

You could, though the combined setup of two heat pumps is still subject to the theoretical limits of a single heat pump. This particular law holds for any conversion from work into a temperature gradient (or the reverse). Any setup that is more efficient would violate the second law of thermodynamics, which results in a nigh infinite supply of energy.

You can make heat pumps 10x more efficient by using 10x smaller increments of temperature, but then you also need to pump each unit of heat 10 times so in the end it doesn't cost less energy to make a bigger temperature gradient.

At each 90 degree jump you might, say, put in one unit of work to move two units of heat.

The problem is at step two you have three units of heat, two of which came from ambient heat.

At step three you have 4.5 units of heat, two of which came from ambient heat.

Step five there are 6.75..and so on.

You're expending a lot of energy moving energy you put in so you get diminishing returns.

The theoretical limit is T_hot / T_change (in absolute units like kelvin). If your change is roughly the hot temperature, there's no benefit.

If you have the liquids with the properties to handle that you could. To make it easier you would have to halve each next heat pump specs, so that the earlier pump can deliver to both the condensor and the evaporator.

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