Heat transfer with internal heat generation using lumped capacitance method

[Precursor]

Homework Statement

The attempt at a solution

The correct approach is to apply the lumped capacitance method. However, in the lumped capacitance problems I've faced before, it never had a heat generation as it does in this problem.

How do I go about solving this?

 

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Think: The block gains heat at a rate of q and losses heat at a rate which is proportional to the temperature difference between itself and the surroundings. Adding heat to a body, what happens to its temperature?

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