$A$ 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 $3 \text{ kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ}\text{C}$ and the entire stored $120$ litres of water is initially cooled to $10^{\circ}\text{C}$. 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 $4.2 \text{ kJ kg}^{-1} \text{K}^{-1}$ and the density of water is $1000 \text{ kg m}^{-3}$)

• A
  $1600$
• B
  $2067$
• C
  $2533$
• D
  $3933$