# heater in a perfectly insulated box

Imagine a perfectly insulated box, placed inside the box is an electric heater. The heater is switched on and the box is left to reach equilibrium with its surroundings. What is the final temperature inside the box?

Clearly a real box would eventually reach an equilibrium temperature with its surroundings at the point where the energy being dissipated by the box matched the energy being added by the heater. If no energy can escape though it seems to imply that the temperature will just keep rising forever which feels wrong to me.

I suspect the answer has something to do with the maximum temperature the heating element can achieve before failing. If we had a heating element that never burnt out though what would the final temperature then be?

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I'm actually glad you asked this question. It is a perfect example of how someone's ordinary logic is just plain physically wrong, which is something that most good basic physics teachers warn about. This isn't the only problem I've encountered in my academic career where a steady-state solution was expected only to end with a reevaluation of the conceptual picture. – Alan Rominger Jul 24 '11 at 20:38