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Kanpur Institute of Technology, KanpurThermal & Hydraulic Machines (EME-309) (EN 3 rd Semester) Question Bank Unit 1 1. An engine cylinder has a piston of area 0.12 m 2 and contains gas at a pressure of 1.5 MPa. The gas expands according to a process which is represented by a straight line on a pressure – volume diagram. The final pressure is 0.15 MPa. Calculate the work done by the gas on the piston if the stroke is 0.30 m. 2. A mass of 1.5 kg of air is compressed in a quasi-static process from 0.1 MPa to 0.7 MPa for which pv = constant. The initial density of air is 1.16 kg/m 3 . Find the work done by the piston to compress the air. 3. A mass of gas is compressed in a quasi-static process from 80 kPa, 0.1 m 3 to 0.4 MPa, 0.03 m 3 . Assuming that the pressure and volume are related by pv n = constant, find the work done by the gas system. 4. Determine the total work done by a gas system following an expansion process as shown in 5. If a gas of volume 6000 cm 3 and at pressure of 100 kPa is compressed quasistatically according to pV 2 = constant until the volume becomes 2000 cm 3 , determine the final pressure and the work transfer. 6. An elastic sphere initially has a diameter of 1 m and contains a gas at a pressure of 1 atm. Due to heat transfer the diameter of the sphere increases to 1.1 m. During the heating process the gas pressure inside the sphere is proportional to the sphere diameter. Calculate the work done by the gas. 7. A stationary mass of gas is compressed without friction from an initial state of 0.3 m 3 and 0.105 MPa to a final state of 0.15 m 3 and .105 MPa, the pressure remaining constant during the process. There is a transfer of 37.6 kJ of heat from the gas during the process. 8. A piston and cylinder machine contains a fluid system which passes through a complete cycle of four processes. During a cycle, the sum of all heat transfers is – 170 kJ. The system completes 100 cycles per min. Complete the following table showing the method for each item, and compute the net rate of work output in kW. Process Q (kJ/min) W (kJ/min ∆E (kJ/min) a - b 0 2, 170 - b – c 21,000 0 - c – d - 2, 100 - - 36,600 d – a - - - 9. The internal energy of a certain substance is given by the following u = (3.56 pv + 84) where u is given in kJ/kg, p is in kPa, and v is in m 3 /kg. A system composed of 3 kg of this substance expands from an initial pressure of 500 kPa and a volume of 0.22 m 3 to a final pressure 100 kPa in a process in which pressure and volume are related by pv 1.2 = constant. (a) If the expansion is quasi-static, find Q, ∆U, and W for the process. (b) In another process the same system expands according to the same pressure-volume relationship as in part (a), and from the same initial state to the same final state as in part (a), but the heat transfer in this case is 30 kJ. Find the work transfer for this process. (c) Explain the difference in work transfer in parts (a) and (b). 10. In a cyclic process, heat transfers are + 14.7 kJ, -25.2 kJ, -3.56 kJ and + 31.5 kJ. What is the net work for this cycle process? 11. The properties of a certain fluid are related as follows u = 196 + 0781t pv = 0.287 (t + 273) where u is the specific internal energy (kJ/kg), t is in o C, p is pressure (kN/m 2 ), and v is specific volume (m 3 /kg). For this fluid, find c v and c p 12. A system composed of 2 kg of the above fluid expands in a frictionless piston and cylinder machine from an initial state of 1 MPa, 100 o C to a final temperature of 30 o C. If there is no heat transfer, find the net work for the process. 13. A mass of 8 kg gas expands within a flexible container so that the p-v relationship is of the form pv 1.2 = const. The initial pressure is 1000 kPa and the initial volume is 1 m 3 . The final pressure is 5 kPa. If specific internal energy of the gas decreases by 40 kJ/kg, find the heat transfer in magnitude and direction. 14. A gas of mass 1.5 kg undergoes a quasi-static expansion which follows a relationship p = a + bv, where a and b are constants. The initial and final pressures are 1000 kPa and 200 kPa respectively and the corresponding volume are 0.20 m 3 and 1.20 m 3 . The specific internal energy of the gas is given by the relation u = 1.5 pv – 85 kJ/kg where p is the kPa and v is in m 3 /kg. Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion. 15. A gas undergoes a thermodynamic cycle consisting of three processes beginning at an initial state where p 1 = 1 bar, V 1 = 1.5 m 3 and U 1 = 512 kJ. The processes are as follows: (i) Process 1-2: Compression with pV = constant to p 2 = 2 bar, U 2 = 690 kJ (ii) Process 2-3: W 23 = 0, Q 23 = - 150 kJ, and (iii) Process 3-1: W 31 = + 50 kJ. Neglecting KE and PE changes, determine the heat interactions Q 12 and Q 31 . 16. The work and heat transfer per degree of temperature change for a system executing a non-flow process are given by c kJ dt W o / 5 . 7 1 = o and . / 5 . 2 1 c kJ dt Q o = o Calculate the change in internal energy of the system as its temperature increases from 120 0 C to 240 0 . 17. An inventor claims to have developed an engine that operates between a source at 450 K and a sink at 280 K, and is capable of delivering 0.15 kWh of work for every 1200 kJ of heat received. As a patent officer, would you issue a patent for such an engine ? 18. A heat engine is supplied with 2512 kJ/min of heat at 650 o C. Heat rejection takes place at 100 o C. Specify which of the following heat rejections represent a reversible, irreversible or impossible result: (i) 867 kJ/min (ii) 1015 kJ/min (iii) 1494 kJ/min 19. An inventor claims that his engine absorbs 300 kJ of energy from a thermal reservoir at 325 K and delivers 75 kJ of work. The inventor also states that his engine has two heat rejections: 125 kJ to a reservoir at 300 K and 100 kJ to a reservoir at 275 K. Check the validity of his claim. 20. A household refrigerator absorbs heat at 2 o C and rejects heat to the surroundings at 50 o C. Its compressor is driven by 3 kW motor and 50 MJ/hr are absorbed at the low temperature. Evaluate the amount of heat rejected per hour and the irreversibility in J/hr. 21. A lump of steel of mass 8 kg at 1000 K is dropped in 80 kg of oil at 300 K. Make calculations for the entropy change of steel, the oil and the universe. Take specific heats of steel and oil as 0.5kJ/kg K and 3.5kJ/kg K, respectively. 22. m 1 kg of water at T 1 is isobarically and adiabatically mixed with m 2 kg of water at T 2 (T 1 > T 2 ). Show that for equal masses of water, the entropy change of the mixture is given by (ds) universe =2mc p log e ( ( ¸ ( ¸ T T T 1 1 1 2 and prove that the change is necessarily positive. 23. A heat engine operates between two thermal reservoirs; source at temperature T1 and sink at temperature T2. If the source and sink are of mass ‘m’ and specific heat ‘c’, set up the following expression for the maximum work output possible W max = m c ( ) T T 2 1 ÷ 2 24. Determine the mass of 0.25 m 3 of wet steam at 5 bar pressure and 0.85 dryness fraction. Proceed to calculate the heat content of 1 m 3 of this steam. 25. A sample of steam at 5 bar is stated to have an enthalpy of 2350 kJ/kg. Make calculations for the specific volume, internal energy and entropy of this sample of steam. 26. Determine the enthalpy, volume, internal energy and entropy of superheated steam at 15 bar pressure and 220 o C. The volume of water may be neglected and take specific heat of superheat equal to 2.2 kJ/kg K. 27. Steam at 10 bar and 200 o C is cooled till it becomes dry saturated and is then throttled to 1 bar pressure. Determine the change in enthalpy and heat transferred during each process. Also find the quality of steam at the end of throttling process. Take c ps = 2.25 kJ/kg K for superheated steam. 28. Steam from a boiler is delivered at an absolute pressure of 15 bar and dryness fraction of 0.95 into a steam superheater in which the steam receives additional heat at constant pressure and its temperature increases upto 300 0 C. Determine the amount of heat added and the change in internal energy for unit mass of steam. 29. Steam is supplied from the boiler at a pressure of 16 bar and 98 percent dry to a steam engine. As the steam flows through the pipeline, its pressure remains constant but it loses 25 kJ/kg of heat due to poor pipe insulation. What would be the condition (temperature and dryness fraction) of steam at the engine end of pipe line? 30. A pressure cooker contains 2 kg of steam at 5 bar pressure and 0.9 dryness fraction. Find the quantity of steam which must be transferred so as the quality of steam becomes 60% dry. Also calculate the pressure and temperature of the steam that exists in the cooker after the heat rejection. 31. A piston cylinder assembly contains one kg of wet steam of quality 0.8 at 0.1 MPa. Energy transfer as heat takes place at constant pressure till the temperature of steam rises to 350 o C. Make calculation for the work done and the heat interaction. 32. Dry saturated steam initially at a pressure of 600 kPa is contained in a thermally insulated cylinder fitted with a frictionless piston. As the piston moves slowly outwards, the steam expands to a pressure of 60 kPa. Calculate the work done by steam. 33. The Simple ideal Rankine Cycle Consider a steam power plant operating on the simple ideal Rankine cycle. The steam enters the turbine at 3 MPa and 350 o C and is condensed in the condenser at a pressure of 75 kPa. Determine the thermal efficiency of this cycle. 34. The ideal Reheat Rankine Cycle Consider a steam power plant operating on the ideal Reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600 o C and is condensed in the condenser at a pressure of 10 kPa. If the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10.4 percent, determine (a) the pressure at which the steam should be reheated and (b) the thermal efficiency of the cycle. Assume the steam is reheated to the inlet temperature of the high-pressure turbine. 35. The ideal Regenerative Rankine Cycle Consider a steam power plant operating on the ideal regenerative Rankine cycle with one open feed water heater. Steam enters the turbine at 15 MPa and 600 o C and is condensed in the condenser at a pressure of 10 kPa. Some steam leaves the turbine at a pressure of 1.2 MPa and enters the open feed water heater. Determine the fraction of steam extracted from the turbine and the thermal efficiency of the cycle.