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Resistors dissipate heat energy with power P=I2R. Since power is defined as energy gained or lost per unit time, we can solve for the energy lost using E=Pt, where E is energy (joules), P is power, and t is time (seconds).

Finally, substituting the definition of power into the equation you get:

E=I2Rt

Answer

With difficulty. The original answer, unfortunately, tells us the work done on the resistor and not the heat transfer from the resistor, which is what the questioner is asking.

The work done on the resistor is the product of the square of the current and the value of its resistance. This will increase the internal energy of the resistor and increase its temperature above that of its surroundings, and heat, by definition, is the energy transferred from the higher temperature resistor to its cooler surroundings.

So there are simply too many unknown variables to take into account: the mass of the resistor, the specific heat capacity of the material from which it's made, the temperature difference between the resistor and its surroundings...

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