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Concentrated fermentation liquid containing 20% (w/w) gluconic acid from an evaporator has a flow rate of 2000 kg/h and a temperature 90 °C. It needs to be cooled to 6 °C in a heat exchanger with cooling water. The cooling water has a flow rate 2700 kg/h and an initial temperature 2 °C. If the cooling water leaves the heat exchanger at 50 °C, what is the rate of heat loss from gluconic acid solution to the surroundings? Assume the heat capacity of gluconic acid is 0.35 cal/g-°C^-1.

(a) 69390.84 kJ/h

(b) 65780.56 kJ/h

(c) 67890.67 kJ/h

(d) 65432.10 kJ/h

The question was asked at a job interview.

Question is from Energy Balance Numericals Without Reactions in section Energy Balance of Bioprocess Engineering

1 Answer

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The correct choice is (a) 69390.84 kJ/h

For explanation I would say: Heat lost by gluconic acid = heat gained by water

[2000(0.2)×(0.35×4.184×1000/1000)×(90-6) + 2000×(0.8)×(376.92-25.2)]+Q

= 2700×(209.33-8.37)×611955.84+Q=542565

Q = -69390.84 kJ/h

Negative sign means heat loss by the system to surrounding.

Hence, heat loss to the surroundings is 69390.84 kJ/h.

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