A water cooler of storage capacity 120 litres can cool water at constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to co

Question

A water cooler of storage capacity 120 litres can cool water at 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 $30^{o} C$ 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 4.2 kJ $k g^{- 1} K^{- 1}$ and the density of water is 1000 kg $m^{- 3}$ )

Question diagram: A water cooler of storage capacity 120 litres can cool water

Options:

Answer:

B

Solution:

$3000 - P = (120 \times 1) (4.2 \times 10^{3}) \frac{d T}{d t}$
$\frac{d T}{d t} = \frac{20}{60 \times 60 \times 3}$
$P = 2067 W$

TestHub · Accepted Answer

3000 - P = 120 × 1 4.2 × 10 3 d T d t d T d t = 20 60 × 60 × 3 P = 2067 W

Physics - Elasticity Question with Solution | TestHub

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