A warm water bath containing 10.0L of water is connected to an ice-water bath with a piece of metal of length L = 2.89 m and cross sectional area A = 1653 cm^2. The metal has a thermal conductivity of Km = 69.6 Wm-1K-1, a specific heat of cm = 380.2 Jkg-1K-1 and a density of ρm = 2591.3 kgm^-3.The warm water bath is initially at a temperature of Th = 64.0 °C.
b) Now lets consider what will happen if the power source heating the warm water bath is switched off. In this case the temperature of the warm water bath will gradually decrease as heat is transferred to the cool water bath. We can describe the heat lost by the warm water bath and the metal rod (the average temperature is just the averages of the temperatures on either side) in time if as: