Solving a Heat Transfer Problem with Lumped Capacitance Method | Homework Help

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The discussion focuses on solving a heat transfer problem using the lumped capacitance method, specifically addressing the challenges posed by heat generation within the system. The key issue is understanding how to account for both the heat gain at a rate of q and the heat loss, which is proportional to the temperature difference with the surroundings. Participants explore the implications of adding heat to a body and its effect on temperature. The conversation emphasizes the need to integrate these factors into the lumped capacitance analysis. Overall, the thread seeks clarity on applying the method in scenarios involving heat generation.
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Homework Statement
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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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