Question

A water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ with 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 $3kW$ 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 $4.2kJ$ ${kg}^{-1}$ $K^{-1}$ and density of water is $1000kg$ $m^{-3}$)

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

Answer 1

The correct option is B $2067$

Heat generated in device in $3$ hours $=P^{\prime }\times t^{\prime }=3\left(3600\right)3\times {10}^3=324\times {10}^{5}J$

Heat used in heating water $=ms\Delta T=120\times 1\times 4200\times (30-10)=100.8\times {10}^{5}J$

Heat absorbed by coolant,
$P\times t=P^{\prime }\times t^{\prime }-ms\Delta T\Rightarrow 324\times {10}^5-100.8\times {10}^5=223.2\times {10}^5$

$P=\frac{223.2\times {10}^5}{3\times 3600}=2067W$