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?