Consider a volume of 100 L of water, initially in liquid form at temperature T_i, to which ΔU = 25 MJ of energy is added from an external reservoir at temperature T_r through a thermal resistance, so that the rate of energy transfer is Q̇ = (1 kW/K)(T_r − T), where T is the instantaneous temperature of the water. The energy is added in two different ways: 

(a) with the water at initial temperature T_i = 100 ^◦C and the external source at temperature T_r = 150 ^◦C; 

(b) with T_i = 0 ^◦C, T_r =75 ^◦C. In each case, compute the time needed to transfer U and the extra entropy produced in this process. Do the comparative results match with the expectation from the discussion of energy transfer at constant temperature?