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It's obviously a one teapot of boiling water can transfer more heat than a cup of boiling water.
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Assuming a teapot full of water has greater volume than a cup of water, then the teapot of water can transfer more heat. In fact, the definition of "heat" is the energy transferred from a hot body to a cold body. The amount of heat depends on three factors: the mass of the substances, the specific heat capacities of the substances and the change in temperature. q=mcΔT. Since the other two factors are the same, the greater mass of water in the teapot accounts for the greater amount of heat.
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