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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 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30oC and the entire stored 120 litres of water is initially cooled to 10oC. 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 kg1 K1 and density of water is 1000 kg m3)

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A
1600
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B
2067
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C
2533
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D
3933
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Solution

The correct option is B 2067
Heat generated in 3 hrs =3(3600)3×103=324×105J

Heat used by water heater =msΔT=120×1×4200×20=100.8×105J

Heat absorbed by coolant = Pt=324×105100.8×105=223.2×105

P=223.2×1053600=2067 W

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