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QJEEAdv16Ph3a85: JEE Advanced 2016 Physics - Class 11 JEEAdv16Ph3a85 Solution: A water cooler of storage capacity 120 litres can cool water at …

A water cooler of storage capacity 120 litres can cool water at a 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°C and the entire stored 120 litres of water is initially cooled to 10°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 : JEE Advanced 2016 Paper 1 Offline Physics - Heat and Thermodynamics Question 38 English

(Specific heat of water is 4.2 kJ kg−1 K−1 and the density of water is 1000 kg m−3)

Multiple Choice Options

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

Step-by-Step Verified Solution

Heat generated in device in 3 h

= Time × power

= 3 × 3600 × 3 × 103 = 324 × 105 J

Heat used to heat water = ms Δ θ

= 120 × 1 × 4.2 × 103 × 20J

Heat absorbed by coolant

Pt = 324 × 105 − 120 × 1 × 4.2 × 103 × 20J

Pt = (325 − 100.8) × 105 J = 223.2 × 105 J

P = 223.2×1053600 = 2067 W

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