Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781259822674
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4.5, Problem 23P
An ideal gas undergoes two processes in a piston–cylinder device as follows:
1–2 Polytropic compression from T1 and P1 with a polytropic exponent n and a compression ratio of r =V1/V2. 2–3 Constant pressure expansion at P3 = P2 until V3 = V1.
- (a) Sketch the processes on a single P-V diagram.
- (b) Obtain an expression for the ratio of the compression-to-expansion work as a function of n and r.
- (c) Find the value of this ratio for values of n = 1.4 and r = 6.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In a heat engine, 2.60 mol of a monatomic ideal gas, initially at 4.00 atm of pressure, undergoes an isothermal expansion, increasing its volume by a factor of 9.50 at a constant temperature of 652.0 K. The gas is then compressed at a constant pressure to its original volume. Finally, the pressure is increased at constant volume back to the original pressure.
What is the heat flow into or out of the gas during process 3? in kJ
A fixed mass of an ideal gas is contained in a piston-cylinder assembly. The pressure and temperature at the initial stage are P1 = 350 kPa and T1 = 600 K. The gas has a molecular weight M = 28 kg / kmol and the constant volume specific heat is Cv = 750 J / kg-K. The initial volume is V1 = 0.50 m^3. The gas is cooled slowly to T2 = 300 K while the pressure remains constant. Find the following:
The cylinder volume V2 after the gas has been cooled to 300 K.
The mass of the gas in the cylinder, m.
The change in the internal energy of the gas, ΔU.
The heat transferred, Q.
The work done, W
Note: Universal gas constant: R prime = 8314.34 J/kmol-K and Specific gas constant: R = R prime / M
1
PROBLEM 3.0 Two and a half kg of an ideal gas with R = 296.9 J/(kg) (K) and c, = 0.7442 kJ/(kg)(K) at a pressure of 827.4
kPa and a temperature of 667°C reject 132.2 kJ of heat at a constant pressure. The gas is then expanded according to
pV1 25 = C to a point where a constant volume process will bring the gas back to its original state. Determine
The heat added in KW
The power in kW for 100 Hz.,
Chapter 4 Solutions
Thermodynamics: An Engineering Approach
Ch. 4.5 - Is the boundary work associated with...Ch. 4.5 - On a P-V diagram, what does the area under the...Ch. 4.5 - An ideal gas at a given state expands to a fixed...Ch. 4.5 - Calculate the total work, in kJ, for process 13...Ch. 4.5 - Calculate the total work, in Btu, produced by the...Ch. 4.5 - Nitrogen at an initial state of 300 K, 150 kPa,...Ch. 4.5 - The volume of 1 kg of helium in a pistoncylinder...Ch. 4.5 - A pistoncylinder device with a set of stops...Ch. 4.5 - A mass of 5 kg of saturated water vapor at 150 kPa...Ch. 4.5 - A frictionless pistoncylinder device contains 16...
Ch. 4.5 - 1 m3 of saturated liquid water at 200C is expanded...Ch. 4.5 - Argon is compressed in a polytropic process with n...Ch. 4.5 - A gas is compressed from an initial volume of 0.42...Ch. 4.5 - A mass of 1.5 kg of air at 120 kPa and 24C is...Ch. 4.5 - During some actual expansion and compression...Ch. 4.5 - A frictionless pistoncylinder device contains 5 kg...Ch. 4.5 - During an expansion process, the pressure of a gas...Ch. 4.5 - A pistoncylinder device initially contains 0.4 kg...Ch. 4.5 - A pistoncylinder device contains 0.15 kg of air...Ch. 4.5 - Determine the boundary work done by a gas during...Ch. 4.5 - 1 kg of water that is initially at 90C with a...Ch. 4.5 - An ideal gas undergoes two processes in a...Ch. 4.5 - A pistoncylinder device contains 50 kg of water at...Ch. 4.5 - Prob. 26PCh. 4.5 - A closed system like that shown in Fig. P427E is...Ch. 4.5 - A rigid container equipped with a stirring device...Ch. 4.5 - Complete each line of the following table on the...Ch. 4.5 - A substance is contained in a well-insulated rigid...Ch. 4.5 - A 0.5-m3rigid tank contains refrigerant-134a...Ch. 4.5 - A 20-ft3 rigid tank initially contains saturated...Ch. 4.5 - A rigid 10-L vessel initially contains a mixture...Ch. 4.5 - A rigid 1-ft3 vessel contains R-134a originally at...Ch. 4.5 - A pistoncylinder device contains 5 kg of...Ch. 4.5 - A pistoncylinder device contains 0.5 lbm of water...Ch. 4.5 - 2 kg of saturated liquid water at 150C is heated...Ch. 4.5 - An insulated pistoncylinder device contains 5 L of...Ch. 4.5 - A 40-L electrical radiator containing heating oil...Ch. 4.5 - Steam at 75 kPa and 8 percent quality is contained...Ch. 4.5 - A pistoncylinder device initially contains 0.6 m3...Ch. 4.5 - An insulated tank is divided into two parts by a...Ch. 4.5 - Two tanks (Tank A and Tank B) are separated by a...Ch. 4.5 - Is the energy required to heat air from 295 to 305...Ch. 4.5 - A fixed mass of an ideal gas is heated from 50 to...Ch. 4.5 - A fixed mass of an ideal gas is heated from 50 to...Ch. 4.5 - A fixed mass of an ideal gas is heated from 50 to...Ch. 4.5 - Is the relation u = mcv,avgT restricted to...Ch. 4.5 - Is the relation h = mcp,avgT restricted to...Ch. 4.5 - What is the change in the internal energy, in...Ch. 4.5 - Neon is compressed from 100 kPa and 20C to 500 kPa...Ch. 4.5 - What is the change in the enthalpy, in kJ/kg, of...Ch. 4.5 - A mass of 10 g of nitrogen is contained in the...Ch. 4.5 - Determine the internal energy change u of...Ch. 4.5 - Determine the enthalpy change h of oxygen, in...Ch. 4.5 - Is it possible to compress an ideal gas...Ch. 4.5 - Nitrogen in a rigid vessel is cooled by rejecting...Ch. 4.5 - Nitrogen at 100 psia and 300F in a rigid container...Ch. 4.5 - A pistoncylinder device containing carbon-dioxide...Ch. 4.5 - A 3-m3 rigid tank contains hydrogen at 250 kPa and...Ch. 4.5 - 1 kg of oxygen is heated from 20 to 120C....Ch. 4.5 - A 10-ft3 tank contains oxygen initially at 14.7...Ch. 4.5 - A 4-m 5-m 7-m room is heated by the radiator of...Ch. 4.5 - An insulated rigid tank is divided into two equal...Ch. 4.5 - An ideal gas contained in a pistoncylinder device...Ch. 4.5 - A 4-m 5-m 6-m room is to be heated by a...Ch. 4.5 - An insulated pistoncylinder device initially...Ch. 4.5 - Argon is compressed in a polytropic process with n...Ch. 4.5 - An insulated pistoncylinder device contains 100 L...Ch. 4.5 - Air is contained in a variable-load pistoncylinder...Ch. 4.5 - A mass of 15 kg of air in a pistoncylinder device...Ch. 4.5 - Prob. 73PCh. 4.5 - A pistoncylinder device contains 2.2 kg of...Ch. 4.5 - A pistoncylinder device contains 4 kg of argon at...Ch. 4.5 - A spring-loaded pistoncylinder device contains 5...Ch. 4.5 - Prob. 78PCh. 4.5 - Prob. 79PCh. 4.5 - A 1-kg block of iron is heated from 25 to 75C....Ch. 4.5 - The state of liquid water is changed from 50 psia...Ch. 4.5 - During a picnic on a hot summer day, all the cold...Ch. 4.5 - An ordinary egg can be approximated as a...Ch. 4.5 - Consider a 1000-W iron whose base plate is made of...Ch. 4.5 - Stainless steel ball bearings ( = 8085 kg/m3 and...Ch. 4.5 - In a production facility, 1.6-in-thick 2-ft 2-ft...Ch. 4.5 - Long cylindrical steel rods ( = 7833 kg/m3 and cp...Ch. 4.5 - An electronic device dissipating 25 W has a mass...Ch. 4.5 - Prob. 90PCh. 4.5 - Prob. 91PCh. 4.5 - Is the metabolizable energy content of a food the...Ch. 4.5 - Is the number of prospective occupants an...Ch. 4.5 - Prob. 94PCh. 4.5 - Prob. 95PCh. 4.5 - Prob. 96PCh. 4.5 - Consider two identical 80-kg men who are eating...Ch. 4.5 - A 68-kg woman is planning to bicycle for an hour....Ch. 4.5 - A 90-kg man gives in to temptation and eats an...Ch. 4.5 - A 60-kg man used to have an apple every day after...Ch. 4.5 - Consider a man who has 20 kg of body fat when he...Ch. 4.5 - Consider two identical 50-kg women, Candy and...Ch. 4.5 - Prob. 103PCh. 4.5 - Prob. 104PCh. 4.5 - Prob. 105PCh. 4.5 - Prob. 106PCh. 4.5 - Prob. 107PCh. 4.5 - Prob. 108PCh. 4.5 - Prob. 109RPCh. 4.5 - Prob. 110RPCh. 4.5 - Prob. 111RPCh. 4.5 - Prob. 112RPCh. 4.5 - Prob. 113RPCh. 4.5 - Consider a pistoncylinder device that contains 0.5...Ch. 4.5 - Prob. 115RPCh. 4.5 - Air in the amount of 2 lbm is contained in a...Ch. 4.5 - Air is expanded in a polytropic process with n =...Ch. 4.5 - Nitrogen at 100 kPa and 25C in a rigid vessel is...Ch. 4.5 - Prob. 119RPCh. 4.5 - A mass of 3 kg of saturated liquidvapor mixture of...Ch. 4.5 - A mass of 12 kg of saturated refrigerant-134a...Ch. 4.5 - Prob. 122RPCh. 4.5 - A pistoncylinder device contains helium gas...Ch. 4.5 - Prob. 124RPCh. 4.5 - Prob. 125RPCh. 4.5 - Prob. 126RPCh. 4.5 - Prob. 127RPCh. 4.5 - Water is boiled at sea level in a coffeemaker...Ch. 4.5 - The energy content of a certain food is to be...Ch. 4.5 - Prob. 130RPCh. 4.5 - An insulated pistoncylinder device initially...Ch. 4.5 - An insulated rigid tank initially contains 1.4 kg...Ch. 4.5 - In order to cool 1 ton of water at 20C in an...Ch. 4.5 - A 0.3-L glass of water at 20C is to be cooled with...Ch. 4.5 - A well-insulated 3-m 4m 6-m room initially at 7C...Ch. 4.5 - Prob. 137RPCh. 4.5 - Prob. 138RPCh. 4.5 - Prob. 140RPCh. 4.5 - A pistoncylinder device initially contains 0.35 kg...Ch. 4.5 - Two 10-ft3 adiabatic tanks are connected by a...Ch. 4.5 - Prob. 143RPCh. 4.5 - Prob. 144RPCh. 4.5 - A 3-m3 rigid tank contains nitrogen gas at 500 kPa...Ch. 4.5 - A 0.5-m3 rigid tank contains nitrogen gas at 600...Ch. 4.5 - A well-sealed room contains 60 kg of air at 200...Ch. 4.5 - A room contains 75 kg of air at 100 kPa and 15C....Ch. 4.5 - Prob. 149FEPCh. 4.5 - A pistoncylinder device contains 5 kg of air at...Ch. 4.5 - Prob. 151FEPCh. 4.5 - A 2-kW electric resistance heater submerged in 5...Ch. 4.5 - Prob. 153FEPCh. 4.5 - 1.5 kg of liquid water initially at 12C is to be...Ch. 4.5 - Prob. 155FEPCh. 4.5 - An ordinary egg with a mass of 0.1 kg and a...Ch. 4.5 - Prob. 157FEPCh. 4.5 - A 6-pack of canned drinks is to be cooled from 18C...Ch. 4.5 - Prob. 159FEPCh. 4.5 - An ideal gas has a gas constant R = 0.3 kJ/kgK and...Ch. 4.5 - A pistoncylinder device contains an ideal gas. The...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Calculate the amount of work necessary for the reversible compression of steam from 1 bar to 10 bar. The compression is to take place in a cylinder fitted with a weightless piston at the constant temperature of 500 oC. Under these conditions we have a superheated vapor. Assume that steam may be treated as an ideal gas. Report your answer in units of kJ/kg using three decimal places. For conversion, note that the molar mass of water is 18.015 g/mol.arrow_forwardAn ideal gas with R=0.062 BTU/lbm-R and Cv=0.158 BTU/lbm-R undergoes a three-cycle in a closed system. From the initial state of 20 psia and 570 R, the gas is compressed at a constant temperature of 1/5 of its initial volume, process 1-2; it is then heated isochorically to state 3, process 2-3; and finally, expands polytropically with index n=1.5 back to its initial state, process 3-1. Determine the pressures, specific volumes and temperatures at cardinal points around the cycle and the cycle thermal efficiency.arrow_forwardA gas with specific volume v₁ 1 m³/Kg and pressure p₁=6bar in a closed system undergoes a thermodynamic cycle which consists of the following three separate processes: 1->2: Isobaric compression to V₂=0.25 m³/Kg 2->3: Isometric heating. 3->1: Isothermal expansion (pV constant) to the initial volume. - Calculate the specific work produced by the gas per cycle. Present your answer in kJ/kg. =arrow_forward
- 3.2 Carbon dioxide (Cp = 871 J/kg.K and Cv = 678 J/kg.K) is compressed from 0.4 m3 at 100 kPa and 14 oC to 0.08 m3 and 690 kPa according to the law PVn = Constant. Determine:(a) The value of the index n(b) The work done during compression(c) The change in internal energy(d) The heat transferred through the cylinder wall, stating whether this is a gain or lossarrow_forwardA well insulated piston-cylinder assembly contains one mole of ideal gas. There are two 3000 kg blocks on this well insulated 0.04 m2 piston. Its starting temperature is 600 K and ambient pressure is 4 bar. The gas is compressed by adding another 3000 kg block. Fixed volume heat capacity is given as (5/2) R. (a) What are the initial and final pressures of the gas in the system?(b) Is the temperature expected to rise or fall? Explain.(c) What is the end temperature?(d) Calculate the values of ∆Ssis and ∆Sis.(e) Does this process violate the second law of thermodynamics? Explain.arrow_forwardKrypton in a closed system is compressed adiabatically from 74 K and 1 bar to a final pressure of 24 bar. What is the final temperature in K? Assume krypton is an ideal gas. From Appendix B in the text, we can assume the heat capacity of krypton is independent of temperature and CP=2.5R , where R is the molar gas constant R=8.314 J/(mol K). For an ideal gas, recall CV=CP−R=1.5R. Report your answer in units of K using three decimal places.arrow_forward
- 2.3 0.2 m3 of a gas at 105 kPa and 27 0C is compressed until the temperature is 282 0C and the pressure is 1.25 MPa. If the specific heats of gas are Cv = 0.653 and Cp = 0.845 kJ/kg.K, determine,(a) Mass of gas(b) The volume at the end of compression(c) The change in internal energyarrow_forwardA quantity of gas (mean molecular weight 36.2) is compressed according to the law pvn = constant, theinitial pressure and volume being 1.03 bar and 0.98 m3 respectively. The temperature at the start of compression is 17°C and at the end it is 115°C. The amount of heat rejected during compression is 3.78 kJ,cp= 0.92. Calculate :(i) Value of n, (ii) Final pressure, (iii) Change in entropy.arrow_forward9. Gas is compressed in an internal combustion engine according to the Law PV1.36 C. If the initial and final temperature of the gas are 30°C and 382°C, respectively, calculate the compression ratio.arrow_forward
- Q1. An assembly of piston cylinder system shown in Figure Q1 had 1 MP pressure and 400°C temperature. The system is cooled to 250°C at a constant pressure and mass of the steam is 0.8 kg. (a) Determine the compression work. (b) If the stopper position is at 40% of the initial volume determine the temperature when the piston immediately touches the stopper and discuss on the nature of the vapor. Steam 0.6 kg 1 MPa 400°C Figure Q1.arrow_forwardA tank of compressed air is at 40°C and 10 atm. 1 third of the gas is removed for inflating a car tire. The tank is allowed to exchange heat with the surroundings to maintain its temperature at all times. What kind of a process is this? What is the pressure remaining in the tank? a. Sketch the problem. b.Draw lines identifying the control volume, or control mass. c.Identify the states with numbers, letters, or descriptions such as “in” and “out”. d.Write down the knowns and unknowns. e.Identify what is being asked for. f.State all assumptions.arrow_forwardAn ideal gas of 4kg mass (MW=3g/mol and k=2.3) contained in a regulated mass system went through three processes in a cycle, one after the other. The initial conditions for the gas were 20kPa and 310K in the first step, and the pressure was isometrically increased by 30kPa. The gas was heated to 400 degrees Celsius using a technique defined by the equation PV3=C. Upon returning to its previous state, it exhibits polytropic behavior. Calculate the change in entropy for each of the processes.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
What is entropy? - Jeff Phillips; Author: TED-Ed;https://www.youtube.com/watch?v=YM-uykVfq_E;License: Standard youtube license