A water cooler of storage capacity 120 litres can cool water at a 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 $$30^\circ C$$ and the entire stored 120 litres of water is initially cooled to $$10^\circ C$$. 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 kg$$^{-1}$$ K$$^{-1}$$ and the density of water is 1000 kg m$$^{-3}$$)