Does it depend on whether you know in advance _when_ you need it back at the hot temperature?
If you don’t think ahead and simply switch the heater back on when you need it, then you need the heater on for_longer_.
That means you have to pay back the energy you lost, but also the energy you lose during the reheating process. Maybe that’s the countervailing effect?
> Hotter objects require more energy to add another unit of heat
Not sure about this. A unit of heat is a unit energy, right? Maybe you were thinking of entropy?
I think you are right about the closed system. When the compressed air spins the dynamo, it will cool, and then absorb heat from the environment. In an ideal, lossless scenario, that heat is equal to the heat given off when it cooled. So maybe you can view it as a battery that stores the energy in the environment?
If you don’t think ahead and simply switch the heater back on when you need it, then you need the heater on for_longer_.
That means you have to pay back the energy you lost, but also the energy you lose during the reheating process. Maybe that’s the countervailing effect?
> Hotter objects require more energy to add another unit of heat
Not sure about this. A unit of heat is a unit energy, right? Maybe you were thinking of entropy?