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Here is one scenario:

I have placed a metal in my room which is at room temperature. Air has little much heat capacity and metals don't like to store heat. Would heat transfer occur? Whatif I set the temperature of both to a certain degree where it crosses heat capacity of metal but not of air?

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Heat transfer only occurs if there’s a difference in temperature. So no, if the temperature of the air and metal is the same, there’s no heat transfer.

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