A water cooler of storage capacity 120 litres can cool water at constant rate of P watts. In a closed…

A water cooler of storage capacity 120 litres can cool water at constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed ${30}^{o}C$ and the entire stored 120 litres of water is initially cooled to ${10}^{o}C$ . The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is:

(Specific heat of water is 4.2 kJ $k{g}^{-1} K^{-1}$ and the density of water is 1000 kg $m^{-3}$ )