Will a pan keep getting hotter and hotter if you put it on low heat?

[jessicahowles]

I read that it won't. That the pan will be at the low heat temperature irregardless of how long you heat it. Is that true?

[ChickenStu]

Once the pan has reached a temperature equivalent to the amount of energy being applied it should stay at a constant temperature. However, most stoves heat up and then cycle on and off to maintain temperature, except for gas (and perhaps induction) which remains on constantly.

[DerekW]

You are applying energy to the entire system - burner, pan, surrounds, what have you. Heat [energy] is going to be lost to the environment. Once the loss rate balances the input rate then a more or less stable state should be reached. What temperature that occurs at will likely vary with different pans for the same burner and input level, due in part at least to different radiant surface areas. Or so I think.

[dcarch]

Temperature of the pan will reach its max when heat lost due to conduction to air and radiation to surrounding surfaces equal to energy generated by the fire.

The theories of Second law of thermodynamics, entropy and blackbody radiation govern this situation.

dcarch

[scott123]

First law of thermodynamics

The first law of thermodynamics says that energy is conserved in any process involving a thermodynamic system and its surroundings. Frequently it is convenient to focus on changes in the assumed internal energy (U) and to regard them as due to a combination of heat (Q) added to the system and work done by the system (W). Taking dU as an incremental (differential) change in internal energy, one writes

dU = δQ - δW,

where δQ and δW are incremental changes in heat and work, respectively. Note that the minus sign in front of δW indicates that a positive amount of work done by the system leads to energy being lost from the system.

Seriously, though... I would say, yes, assuming we're referring to an electric element, the thermostat will cut off at a set (lower) temperature, regardless of whether the pan is on it or not.

[Fat Guy]

Whether the burner is low or high, a pot or pan will eventually reach a maximum temperature and go no higher. It's just that on a high flame the pan may be destroyed before reaching equilibrium, whereas this isn't a concern with most pans (nonstick could be an exception) on a low setting.

[s0rce]

Even if you know nothing about thermodynamics you can think about this problem pretty simply. If you were to leave a pan on a hypothetical burner where the temperature does keep increasing would you expect it to just increase forever and melt the pan, then the store itself and your entire house... probably not. So we can surmise that at some point the pan being heated reaches equilibrium with its surroundings.