A water cooler of storage capacity $120$ litres can cool water at constant rate of $P$ $\mathrm{W}$. 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 $3$ $\mathrm{kW}$ of heat (thermal load). The temperature of water fed into the device can not 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 $\mathrm{W}$) for which the device can be operated for $3$ hours is:

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