GATE 2024 ME – Question 49
A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1 kg/s with an inlet temperature of 30 °C. The steam in the condenser shell condenses at the rate of 430 kg/s at a temperature of 50 °C. If the heat of vaporization is 2.326 MJ/kg and specific heat of water is 4 kJ/(kg.K), the effectiveness of the heat exchanger is ________ (*rounded off to 3 decimal places*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.615 to 0.635
Explanation
The heat given up by the condensing steam is $Q = 430 \times 2326 = 1\,000\,180$ kW. The water has the smaller heat capacity rate, $C_{min} = 20000 \times 1 \times 4 = 80\,000$ kW/K (the condensing side has an infinite one). The most heat that could be transferred is $C_{min}(50 - 30) = 1\,600\,000$ kW. So the effectiveness is $\varepsilon = \frac{1\,000\,180}{1\,600\,000} = 0.625$.