Question

A water cooler of storage capacity $120$ liters can cool water at a constant rate of $P$ watts. In a closed circular system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly $3kW$ 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 $4.2kJk{g}^{-1}{K}^{-1}$ and the density of water is $1000kg{m}^{-3}$ )

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

Answer 1

Answer: (B)

Rate of heat extracted by water $=\left(\frac{ms\Delta T}{\Delta t}\right)$
Power by cooler $+\frac{ms\Delta T}{\Delta t}=H$
$P+\frac{ms\Delta T}{\Delta t}=H$
For $P_{\min }$ in $\Delta t=3hrs$
$P=H-\frac{ms\Delta T}{\Delta t}$
$P=3\times 10^3-\frac{P\times 120\times 10^{-3}\times 4.2\times 10^3\times (30-10)}{3\times 60\times 60}$
$P=2067$ Watt