All heat that is lost must be replaced (we must input enough heat that the device returns to T_initial)
Hotter objects lose heat faster, so the longer we delay restoring temperature (for a fixed resume time) the less heat is lost that will need replacement.
Hotter objects require more energy to add another unit of heat, so the cooler we allow the device to get before re-heating (again, resume time is fixed) the more efficient our heating can be.
There is no countervailing effect to balance, preemptive heating of a device before the last possible moment is pure waste no matter the conditions (although the amount of waste will vary a lot, it will always be a positive number)
Even turning the heater off for a millisecond is a net gain.
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?
Hotter objects lose heat faster, so the longer we delay restoring temperature (for a fixed resume time) the less heat is lost that will need replacement.
Hotter objects require more energy to add another unit of heat, so the cooler we allow the device to get before re-heating (again, resume time is fixed) the more efficient our heating can be.
There is no countervailing effect to balance, preemptive heating of a device before the last possible moment is pure waste no matter the conditions (although the amount of waste will vary a lot, it will always be a positive number)
Even turning the heater off for a millisecond is a net gain.