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But all the examples you give have a heat source of high temperature and dense energy, and a lot of energy is lost in it's transformation, as illustrated by the combustion engine. How can heat be a good energy storage if so much is lost when you want to use it?
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If it's free to collect (solar) then efficiency matters a lot less.
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It isn't just the cost to collect, it is also the cost to store. Heat is easy and safe to store at just above room temperature in rocks - but you need a lot of rocks. Just to heat my house for a few days would need tons of rock at temperatures I'd allow in my house (I have kids and so I worry they will open the rock container and get burnt). Rocks are not free. You can also use water for storage, but again you have the issue needing a tank (and water is a drowning hazard, plus the worry about leaks...)
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Square cube law will optimise heat storage. These Finnish sand based heat batteries are a prime small-scale example.
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