Practice Problems Set 8

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IIT Kanpur *

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201A

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Mechanical Engineering

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Nov 24, 2024

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INDIAN INSTITUTE OF TECHNOLOGY KANPUR ESO 201A: Thermodynamics (2023-24 I Semester) Instructor: Dr Avinash Kumar Agarwal Practice Problems - Set 8 --------------------------------------------------------------------------------------------------------------------------- Question 1 : A heat engine that rejects waste heat to a sink at 510 R has a thermal efficiency of 25 percent and a second-law efficiency of 50 percent. Determine the temperature of the source that supplies heat to this engine. (Ans: 1020 R) Fig. 1 Question 2: In an ice-making plant, water at 0°C is frozen at atmospheric pressure by evaporating saturated R-134a liquid at – 16°C. The refrigerant leaves this evaporator as a saturated vapor, and the plant is sized to produce ice at 0°C at a rate of 5500 kg/h. Determine the rate of entropy generation in this plant. (Ans: 0.115 kW/K) Fig. 2 Question 3: Steam expands in a turbine steadily at a rate of 40,000 kg/h, entering at 8 MPa and 500°C and leaving at 40 kPa as saturated vapor. If the power generated by the turbine is 8.2 MW, determine the rate of entropy generation for this process. Assume the surrounding medium is at 25°C. (Ans: (a) 11.4 kW/K)

Fig. 3 Question 4: A 0.8-m3 insulated rigid tank contains 1.54 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 135 kPa. Determine (a) the actual paddle-wheel work done during this process and (b) the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take T0 = 298 K. (Ans: (a) 101 kJ, (b) 7.18 kJ) Fig. 4 Question 5: A piston – cylinder device initially contains 1.4 kg of refrigerant-134a at 100 kPa and 20°C. Heat is now transferred to the refrigerant from a source at 150°C, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 120 kPa. Heat transfer continues until the temperature reaches 80°C. Assuming the surroundings to be at 25°C and 100 kPa, determine (a) the work done, (b) the heat transfer, (c) the exergy destroyed, and (d) the second-law efficiency of this process. (Ans: (a) 0.497 kJ, (b) 67.9 kJ, (c) 14.8 kJ, (d) 26.2 %) Question 6: Steam enters a turbine at 9 MPa, 600°C, and 60 m/s and leaves at 20 kPa and 90 m/s with a moisture content of 5 percent. The turbine is not adequately insulated, and it estimated that heat is lost from the turbine at a rate of 220 kW. The power output of the turbine is 4.5 MW. Assuming the surroundings to be at 25°C, determine (a) the reversible power output of the turbine, (b) the exergy destroyed within the turbine, and (c) the second-law efficiency of the turbine. (d) Also, estimate the possible increase in the power output of the turbine if the turbine were perfectly insulated. (Ans: (a) 5451 kW, (b) 951 kW, (c) 82.6%, (d) 67.8 kW)

Fig. 5 Question 7: A geothermal power plant uses geothermal liquid water at 150°C at a rate of 210 kg/s as the heat source, and it produces 5.1 MW of net power in an environment at 25°C. If 7.5 MW of exergy entering the plant with the geothermal water is destroyed within the plant, determine (a) the exergy of the geothermal water entering the plant, (b) the second-law efficiency, and (c) the exergy of the heat rejected from the plant. (Ans: (a) 18.46 MW, (b) 27.6%, (c) 5.86 MW) Question 8 : Liquid water at 200 kPa and 15°C is heated in a chamber by mixing it with superheated steam at 200 kPa and 200°C. Liquid water enters the mixing chamber at a rate of 4 kg/s, and the chamber is estimated to lose heat to the surrounding air at 25°C at a rate of 600 kJ/min. If the mixture leaves the mixing chamber at 200 kPa and 80°C, determine (a) the mass flow rate of the superheated steam and (b) the wasted work potential during this mixing process. (Ans: (a) 0.429 kg/s, (b) 202 kW) Fig. 6

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