Problem 1. (12 points) Consider a volume of coffee in a ceramic mug at temperature353 K in a 300 Kroom. In this problem, we'll attempt to estimate the relative importance of radiation versus conduction in cooling the coffee. (a) (4 points) Calculate the net power radiated by the top surface of the coffee. (The Stefan- Boltzmann constant is a 5.7 X 10_8W/(m2 K4)) For a typical coffee mug we can estimate Atop 3.8 X 10'3 m2. (The coffee has an emissivity very close to 1, so treat it as a black body.) (13) (8 points) Model heat conduction through the ceramic coffee mug (thermal conductivity about 3.8 W/ (m K)) as if it were one-dimension, with the mug having a cross-sectional area of 0.021 m2 and a thickness of 6 mm. Calculate the rate Peond of heat transfer by conduction, and nd the ratio Prad /Pcond. Based on this simplified calculation, which form of heat transfer is more important