A 1 kg sphere of iron at 1000 degrees Celsius is quenched in a 10 kg bath of oil at 100 degrees Celsius. Assume that no heat is lost to the surroundings and the temperature of the oil is uniform.
a) Calculate the final equilibrium temperature of the iron sphere and the oil. Assume the heat capacities of iron and oil to be 450 J/kg-K and 1800 J/kg-K, respectively.
b) Plot the temperature of the iron sphere as a function of time and calculate the temperature of the iron sphere after 5 minutes. The heat transfer coefficient between the surface of the iron sphere and the oil is 245 W/m^2-K. The density and thermal conductivity of iron are 7874 kg/m^3 and 80W/m-K, respectively.