Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Transcription

1 Problems of Practices Of Basic and Applied Thermodynamics First Law of Thermodynamics Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us 1. A pressure vessel is connected, via a valve, to a gas main in which gas is maintained at a constant pressure and temperature of 1.4 MN/m 2 and 85 C respectively. The pressure vessel is initially evacuated. The valve is opened and a mass of 2.7 kg of gas passes into the pressure vessel. The valve is closed and the pressure and temperature of the gas in the pressure vessel are then 700 kn/m 2 and 60 C, respectively. Determine the heat transfer to or from the gas in the vessel. Determine the volume of gas before transfer. For the gas, take Cp = 0.88 kj/kg K, Cv = 0.67 kj/kg K. Neglect the velocity of the gas in the main. 2. A spherical balloon of 1 m diameter contains a gas at 200 kpa and 300 K. The gas inside the balloon is heated until the pressure reaches 500 kpa. During the process of heating, the pressure is proportional to the diameter of the balloon. Determine the work done by the gas inside the balloon. 3. The heat capacity at constant pressure of a certain system is a function of temperature only and may be expressed as C p J/ C t 100 where t is the temperature in C. The system is heated while it is maintained at a pressure of 1atmosphere until its volume increases from 2000 cm 3 to 2400 cm 3 and Copyright by Brij 2013 Page 1

2 2 Problems of Practices on First Law of Thermodynamics its temperature increases from 0 C to 100 C. (i) Find the magnitude of heat interaction. (ii) How much does the internal energy of the system increase? 4. An ideal gas is heated at constant volume until its temperature is 3 times the original temperature, then it is expanded isothermally till it reaches its original pressure. The gas is then cooled at constant pressure till it is restored to the original state. Determine the net work done per kg of gas if the initial temperature is 350 K. 5. A compressed air bottle of volume 0.15 m 3 contains air at 40 bar and 27 C. It is used to drive a turbine which exhausts to atmosphere at 1 bar. If the pressure in the bottle is allowed to fall to 2 bar, determine the amount of work that could be delivered by the turbine. 6. A cylinder contains one kg of water and steam at a pressure of 3.8 bar and 0.4 dry. Heat is supplied at constant volume until the pressure reaches to 10 bar. The steam is then expanded according to the law pv = constant, until the pressure is 2 bar. Calculate (i) Heat transfer during constant volume heating. (ii) Heat transfer during pv = constant expansion. (iii) Temperature of steam after the expansion. 7. A closed system executes a reversible cycle consisting of six processes. During processes 1-2 and 3-4 the system receives 1000 kj and 800 kj of heat, respectively, at constant temperatures of 500K and 400 K, respectively. Processes 2-3 and 4-5 are adiabatic expansions in which the system temperature is reduced from 500 K to 400 K and from 400 K to 300 K, respectively. During process 5-6 the system rejects heat at a constant temperature of 300 K process 6-1 is an adiabatic compression process. Determine the work done by the system during the cycle and the thermal efficiency of the cycle. 8. An evacuated bottle of 0.5 m 3 volume is slowly filled from atmospheric air at bars until the pressure inside the bottle also becomes bars. Due to heat transfer, the temperature of air inside the bottle after filling is equal to the atmospheric air temperature. Determine the amount of heat transfer. 9. A Piston-cylinder device contains 3 kg of wet steam at 1.4 bars. The initial volume is 2.25 m 3. The steam is heated until its temperature reaches 400 C. The piston is free to move up or down unless it reaches the stops at the top. When the piston is up against the stops the cylinder volume is 4.65 m 3. Determine the amounts of work and heat transfer to or from steam. 10. A compressed air bottle of 0.05 m 3 volume contains air at 3.5 atm pressure. This air is used to drive a turbo-generator supplying power to a device which consumes 5 W. Calculate the time for which the device can be operated if the actual output of the turbo-generator is 60 percent of the, maximum theoretical output. The ambient pressure is 1 atm. For air, (Cp/CV) = kg of air at 1.50 bar pressure and 87 C temperature at condition 1 is compressed polytropically to condition 2 at pressure 7.50 bar. Index of compression being 1.2. It is then cooled at constant pressure in condition 3 and then finally heated at constant temperature to its original condition 1. Find the net work done and heal transferred. 12. A rigid tank of m 3 volume contains air at bar and 21.1⁰C. The tank is equipped with a relief valve that opens at a pressure of bar and remains open Copyright by Brij 2013 Page 2

3 Problems of Practices of Basic and Applied Thermodynamics By Brij Bhooshan 3 until the pressure drops to bar. If a fire causes the valve to operate once as described, determine the air temperature just before the valve opens and the mass of air lost due to the fire. Assume that the temperature of the air remains constant during discharge and air in the tank behaves as an ideal gas. 13. A scales are so chosen that a reversible cycle plots clockwise as a circle on the T-S plane. The minimum and maximum values of the temperature are 305 and 627 K and the entropy 1.23 and 2.85 kj/k, respectively. Find the cycle work and efficiency. 14. A stationary mass of gas is compressed without friction from an initial state of 0.3 m 3, MPa to a final state of 0.15 m 3 and MPa, the pressure remaining constant. During the process, an amount of 37.6 kj of heat is rejected by the gas. What is the change in internal energy of the gas during the process? 15. State the Zeroth Law of Thermodynamics and highlight its significance. 16. For an isothermal process, show that: 17. In a system executing a non flow process the work and heat per degree change of temperature are given by dw/dt = 200W-s/ C and dq/dt = 160 J/ C. What will be the change in internal energy of the system when its temperature changes from T1 = 55 C to T2 = 95 C? 18. A balloon is filled with hydrogen. It has 1000 m 3 volume at temperature 300 K and pressure 100 kpa. Determine the payload that can be lifted with the balloon. 19. A closed cylinder of 0.25 m diameter is fitted with a light frictionless piston. The piston is retained in position by a catch in the cylinder wall and the volume on one side of the piston contains air at a pressure of 750 kn/m 2. The volume on the other side of the piston is evacuated. A helical spring is mounted co-axially with the cylinder in this evacuated space to give a force of 120 N on the piston in this position. The catch is released and the piston travels along the cylinder until it comes to rest after a stroke of 1.2 m. The piston is then held in its position of maximum travel by a ratchet mechanism. The spring force increases linearly with the piston displacement to a final value of 5 kn. Calculate the work done by the compressed air on the piston. 20. Consequent upon first law of thermodynamics, show that the heat is a path function. 21. An imaginary engine receives heat and does work on a slowly moving piston at such rates that the cycle of operation of 1 kg of working fluid can be represented as a circle 10 cm in diameter on a p-v diagram on which 1 cm = 300 kpa and 1 cm = 0.1 m 3 /kg. Determine how much work is done by each kg of working fluid for each cycle of operation. If the heat rejected by the engine in a cycle is 1000 kj per kg of working fluid, find the thermal efficiency of the engine. 22. A fluid, contained in a horizontal cylinder fitted with a frictionless leakproof piston, is continuously agitated by means of stirrer passing through the cylinder cover. The cylinder diameter is 0.40 m. During the stirring process lasting 10 minutes, the piston slowly moves out a distance of m against the atmosphere. The net work done by the fluid during the process is 2 kj. The speed of the electric motor driving the stirrer is 840 r.p.m. Determine the torque in the shaft and the Copyright by Brij 2013 Page 3

4 4 Problems of Practices on First Law of Thermodynamics power output of the motor. 23. What is meant by free expansion process and how does it differ from throttling process? One kilogram of a gas having pressure P1 and temperature T1, is enclosed in an insulated box of volume V1. It is allowed to expand freely till its volume increases to V2 = 2V1. Show the process on P-V and T-S diagrams and determine Q, ΔV, W and ΔS for the free expansion process. Comment on the results. 24. The ratio of heat transfer to work transfer in the process of an air compressor reciprocating type is 1/4. If the compression follows pv n = constant, what is the value of n? Derive the equation that you use. In such a compression process the work required is 200 kj/kg and the specific heat at constant volume is 0.75 kj/kg K. What rise of temperature is expected at the end of compression process? 25. A gas is confined to a cylinder by a spring loaded frictionless piston, so that the pressure in the fluid is a linear function P = a + bv. The internal energy of the gas is given by U = 34 + PV(3.15) where U is in kj, P in kpa and V in m 3. If the gas changes from an initial state of 170 kpa, 0.03 m 3 to a final state of 400 kpa, 0.06 m 3 with no work other than that done on piston, find the direction and magnitude of work and heat transfer. 26. Show that when a gas expands behind a piston according to the law Pv γ = constant, the heat transfer, change in internal energy and work done are in the ratio (γ- n): (n -1): (γ- 1) and that the effective specific heat C for an expansion of this kind is times its specific heat at constant volume CV. 27. Air at 100 KPa and 300 C is contained in a piston cylinder arrangement as shown in fig.(l): The cylinder is perfectly insulated and piston is held in position by stops at A. The outside pressure is atm. The stops A are suddenly removed and the air allowed to expand till the piston stops at stops B. The volume increases to 1.5 times the initial value. Assume that the friction between piston and cylinder is zero; calculate the final pressure and temperature of air. State your assumptions clearly. 28. Prove that system energy is a property. 29. A large air tank has a volume of 3.37 m 3. Determine the number of small containers that can be filled from the air tank. Given ttank = 26.6 C; Ptank = 6.5 kg/cm 2,Vcontainer = m 3, tcontainer = 21 C and Pcontainer = 1.35 kgf/cm 2. For air, assume R = 29.7 kgm/kgk. 30. A pressure vessel is connected, via a valve, to a gas main in which a gas is maintained at constant pressure and temperature of 15 kgf/cm 2 and 80 C respectively. The pressure vessel is initially evacuated. The valve is opened and a mass of 3 kg of gas passes into the pressure vessel. The valve is closed and the pressure and temperature of the gas in the pressure vessel is then 7 kgf/cm 2 and 60 C, respectively. Determine- (i) the heat transfer to or from the gas in the vessel; Copyright by Brij 2013 Page 4

5 Problems of Practices of Basic and Applied Thermodynamics By Brij Bhooshan 5 (ii) the volume of the pressure vessel; (iii) the volume of the gas before transfer. For the gas take Cp = 0.22kcal/kgK and Cv=0.16 kcal/kgk. 31. A rigid vessel of volume 0.3 m 3 contains perfect gas at a pressure of 1 kgf/cm 2. In order to reduce the pressure in the vessel it is connected to an extraction pump. The volume flow rate of the gas leaving the vessel is constant at m 3 /min. Assuming the temperature of the gas to remain constant, calculate (i) Time taken to reduce the pressure in the vessel to 035 kgf/cm 2 ; (ii) Magnitude and sense of heat transfer between the vessel and the surroundings during the time. Derive any formula you use. Copyright by Brij 2013 Page 5