Question: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modication of (2)

The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modication of (2) is

dT/dt = kS(T - T_m),

where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 150° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 100° F. If T_m = 70° F, then what is the temperature of the coffee in cup B after 30 min?

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