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Expert Solution

The temperature rise per second is equal to the heat supplied per second (i.e., the power supplied if there are no losses) divided by the total heat capacity of the water and its container:

deltaT/deltat = (deltaQ/deltat)/Ctot, = P/Ctot .

The total heat capacity is Ctot = CW + Cent,

provided the water and container both have the same instantaneous temperature. (This assumes that heat is supplied sufficiently slowly that the water and container share it and stay in instantaneous thermal equilibrium.) For the paper cup used in the microwave oven, Ccnt= 0, whereas for the pan used on the stove burner, Ccnt = 1.1kJ/K. Thus, the rate of temperature rise is - 775 W/Cw for the microwave and 2.0 kW/(Cw + 1.1 kJ/K) for the stove burner.

When CW = mwcw is small, the microwave is faster, whereas when Cw is large, the stove burner is faster. The rates of temperature rise are equal for Cw = mw x (4.184 kJ1kg.K) = (1.1 kJ/K)(0.775)/(1 - 0.775) = 3.788 kJ/K. Therefore, mw = (3.788 kJ/K)/ (4.184 kJ/kg-K) = 0.9055 kg

genius_generous answered 1 week ago

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