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A milk chilling unit can remove heat from the milk at the rate of 41.87 MJ/h. Heat leaks into the milk from the surroundings at an average rate of 4.187 MJ/h. Find the time required for cooling a batch of 500 kg of milk from 45°C to 5°C. Take the cp of milk to be 4.187 kJ/kg K.

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Heat to be removed (H) = mst

= 500 × 4.187 × (45-5) kJ

= 83.740 MJ

Net rate of heat removal = Hrej - Hleak

= (41.87 - 4.187) MJ / h

= 37.683 MJ / h

∴ Time required = \(\frac{83.740}{37.683}\) hr

= 2 hr. 13 min. 20 sec.

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