A college professor keeps 0.25 L (0.00025 m^3) of hot coffee in a thick styrofoa

Question

A college professor keeps 0.25 L (0.00025 m^3) of hot coffee in a thick styrofoam container. The container is 0.6 cm thick and has a total surface area of 0.025 m^2. Assume that the temperature of the inner wall surface is 85 C and that of the outer surface is 35 C. Assume the coffee's density and specific heat are the same as water's, 1000 kg/m^3 and 4184 J/Kg/C, and the thermal conductivity of styrofoam is 0.04 W/m/C.

a) at what rate is heat flowing out through the walls of the container?

b) At that rate, how long would it take for the temperature of the cofee to decrease by 1 Celsius degree?

Explanation / Answer

Area = (1.2 m)•(1.8 m) = 2.16 m2. We will also need to give attention to the unit on thickness (d). It is given in units of cm; we will need to convert to units of meters in order for the units to be consistent with that of k and A. d = 6.2 mm = 0.0062 m Now we are ready to calculate the rate of heat transfer by substitution of known values into the above equation. Rate = (0.27 W/m/°C)•(2.16 m2)•(21°C - -4°C)/(0.0062 m) Rate = 2400 W (rounded from 2352 W) It is useful to note that the thermal conductivity

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