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Question

A water cooler of storage capacity 120 litres can cool water at a constant rate of P. In a closed circulation system (as shown schematically in this figure), the water from the cooler is used to cool an external device that constantly generates 3 kW of power (thermal load). The temperature of the water fed into the device cannot exceed 30C and the entire 120 litres of water is initially cooled to 10C. The entire system is thermally insulated. The minimum value of P for which the device can be operated for 3 hours (taking the specific heat capacity of water =4.2 kJ kg1K1 and the density of water =1000 kg m3) is


A
1600 W
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B
2067 W
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C
2533 W
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D
3933 W
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Solution

The correct option is B 2067 W
Given that,
Initial temperature, θ1 =10C
Final temperature, θ2 =30C
Mass of water in cooler =120 kg
Change in temperature, Δθ=20C

Heat generated by the device =(3 kW)(3 hrs)=3×103×3×3600 J
=324×105 J
Heat absorbed by water =mcwΔθ=(120)(4200)(20)=100.8×105 J
Heat absorbed by the coolant,
=Pt=(324×105100.8×105) J
P=223.2×105 J3×3600s=2067 W
is the minimum rate of cooling.

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