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How much energy is 'lost' in the expansion valve in a typical heat pump?

Isn't it worth putting a turbine in there to recoup the energy released as a high pressure liquid passes through a small hole?

Even if it's only 10%, that's still 10% of the energy use of your home for a decade - surely that pays for a micro turbine (which need not be particularly complex - the same design used in those $3 light up novelty faucets would probably work.).

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I worked for a chair that studied this kind of stuff - your best bet is to figure out how to reduce the temperature lift. Due to the way the Carnot equation works (at least, that's what I _think_ it's called, this is all a while ago), that really get's the heatpump efficiency singing.

reduce the heating temperature by increasing the area you're radiating from - floor heating / ceiling heating is way more efficient than radiators since you can deliver the same amount of heat at much lower temperatures to the space.

Putting fans on radiators should also increase the amount of heat that can be transferred, right?

right, you can use low temp radiators or fancoils than are built for this use cases.

There are various research projects looking at storing waste heat, often for the purpose of more efficient defrosting.

https://www.nature.com/articles/s44172-022-00018-3

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