Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7.13, Problem 225RP
The polytropic or small stage efficiency of a turbine η∞, T is defined as the ratio of the actual differential work done to the isentropic differential work done by the fluid flowing through the turbine, η∞, T = dh/dhs. Consider an ideal gas with constant specific heats as the working fluid in a turbine undergoing a process in which the polytropic efficiency is constant. Show that the temperature ratio across the turbine is related to the pressure ratio across the turbine by
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the entropy production and determine if the cycle operates irreverisbly, reverisbly, or impossibly.
A refrigeration cycle operates between the freezer compartment at 268K and the ambient air at 295K. The rate of heat transfer from the freezer compartment is 8000 kJ/h and the power input for the cycle is 3200 kJ/h. Determine the entropy production for this cycle in kJ/K·h (do not convert h to s). Enter the answer without units, but with a minus sign if applicable.
This cycle operates
irreversibly
reversibly
impossibly.
4. Steam enters the condenser of a steam power plant at 20000 kPa and a quality of 95 percent with a mass flow rate of 20 Mg/h. It is to be cooled by water from a nearby river in circulating the water through the tubes within the condenser. To prevent thermal pollution, the river water is not allowed to experience a temperature rise above 10oC. If the steam is to leave the condenser as saturated liquid at 20000 Pa, determine the mass flow rate of the cooling water required
Refrigerant 134a enters an air-cooled condenser at 12 bars and 60°C, and leaves as a
saturated liquid at 12 bars. Atmospheric air at 35°C is blown over the condenser tubes
and leaves at 45°C. The heat transfer between the two fluid streams equals 25 MJ/h.
Changes in kinetic and potential energy are negligible. Make any reasonable assumptions
if necessary. Determine
(a) the mass flow rates for the R-134a and the air, in kg/h,
Hint: Use the energy conservation on each of the { uid streams separately.
(b) the entropy production rate in the condenser, in kJ h-'K-1,
Hint: Use the entropy balance over the whole condenser.
(c) the change in kinetic energy for R-134a if the pipe diameter is 2.0 cm, in kJ/h
(d) Draw the T-s diagram for the process for R-134a.
Air
P=1 atm
T3= 35°C
%3!
Ref
rant 134a
R-134a
P = 12 bar
2
T
= 60°C
R-134a
P2 = 12 bar
Air
4-
T4= 45°C
Chapter 7 Solutions
Thermodynamics: An Engineering Approach
Ch. 7.13 - Prob. 1PCh. 7.13 - Does the cyclic integral of heat have to be zero...Ch. 7.13 - Is a quantity whose cyclic integral is zero...Ch. 7.13 - Prob. 4PCh. 7.13 - Prob. 5PCh. 7.13 - How do the values of the integral 12Q/T compare...Ch. 7.13 - The entropy of a hot baked potato decreases as it...Ch. 7.13 - When a system is adiabatic, what can be said about...Ch. 7.13 - Prob. 9PCh. 7.13 - A pistoncylinder device contains helium gas....
Ch. 7.13 - A pistoncylinder device contains nitrogen gas....Ch. 7.13 - A pistoncylinder device contains superheated...Ch. 7.13 - The entropy of steam will (increase, decrease,...Ch. 7.13 - Prob. 14PCh. 7.13 - Prob. 15PCh. 7.13 - Prob. 16PCh. 7.13 - Steam is accelerated as it flows through an actual...Ch. 7.13 - Prob. 18PCh. 7.13 - Prob. 19PCh. 7.13 - Prob. 20PCh. 7.13 - Heat in the amount of 100 kJ is transferred...Ch. 7.13 - In Prob. 719, assume that the heat is transferred...Ch. 7.13 - 7–23 A completely reversible heat pump produces...Ch. 7.13 - During the isothermal heat addition process of a...Ch. 7.13 - Prob. 25PCh. 7.13 - During the isothermal heat rejection process of a...Ch. 7.13 - Prob. 27PCh. 7.13 - Prob. 28PCh. 7.13 - Two lbm of water at 300 psia fill a weighted...Ch. 7.13 - A well-insulated rigid tank contains 3 kg of a...Ch. 7.13 - The radiator of a steam heating system has a...Ch. 7.13 - A rigid tank is divided into two equal parts by a...Ch. 7.13 - 7–33 An insulated piston–cylinder device contains...Ch. 7.13 - Prob. 34PCh. 7.13 - Prob. 35PCh. 7.13 - Onekg of R-134a initially at 600 kPa and 25C...Ch. 7.13 - Refrigerant-134a is expanded isentropically from...Ch. 7.13 - Prob. 38PCh. 7.13 - Refrigerant-134a at 320 kPa and 40C undergoes an...Ch. 7.13 - A rigid tank contains 5 kg of saturated vapor...Ch. 7.13 - A 0.5-m3 rigid tank contains refrigerant-134a...Ch. 7.13 - Prob. 44PCh. 7.13 - Prob. 45PCh. 7.13 - Steam enters an adiabatic diffuser at 150 kPa and...Ch. 7.13 - Prob. 47PCh. 7.13 - An isentropic steam turbine processes 2 kg/s of...Ch. 7.13 - Prob. 50PCh. 7.13 -
7–51 0.7-kg of R-134a is expanded isentropically...Ch. 7.13 - Twokg of saturated water vapor at 600 kPa are...Ch. 7.13 - Steam enters a steady-flow adiabatic nozzle with a...Ch. 7.13 - Prob. 54PCh. 7.13 - In Prob. 755, the water is stirred at the same...Ch. 7.13 - A pistoncylinder device contains 5 kg of steam at...Ch. 7.13 - Prob. 57PCh. 7.13 - Prob. 59PCh. 7.13 - A 50-kg copper block initially at 140C is dropped...Ch. 7.13 - Prob. 61PCh. 7.13 - Prob. 62PCh. 7.13 - A 30-kg aluminum block initially at 140C is...Ch. 7.13 - A 30-kg iron block and a 40-kg copper block, both...Ch. 7.13 - An adiabatic pump is to be used to compress...Ch. 7.13 - Prob. 67PCh. 7.13 - Can the entropy of an ideal gas change during an...Ch. 7.13 - An ideal gas undergoes a process between two...Ch. 7.13 - Prob. 72PCh. 7.13 - Prob. 73PCh. 7.13 - Prob. 74PCh. 7.13 - Prob. 75PCh. 7.13 - A 1.5-m3 insulated rigid tank contains 2.7 kg of...Ch. 7.13 - An insulated pistoncylinder device initially...Ch. 7.13 - A pistoncylinder device contains 0.75 kg of...Ch. 7.13 - Prob. 80PCh. 7.13 - 7–81 Air enters a nozzle steadily at 280 kPa and...Ch. 7.13 - A mass of 25 lbm of helium undergoes a process...Ch. 7.13 - One kg of air at 200 kPa and 127C is contained in...Ch. 7.13 - Prob. 85PCh. 7.13 - Air at 3.5 MPa and 500C is expanded in an...Ch. 7.13 -
7–87E Air is compressed in an isentropic...Ch. 7.13 - An insulated rigid tank is divided into two equal...Ch. 7.13 - An insulated rigid tank contains 4 kg of argon gas...Ch. 7.13 - Prob. 90PCh. 7.13 - Prob. 91PCh. 7.13 - Prob. 92PCh. 7.13 - Air at 27C and 100 kPa is contained in a...Ch. 7.13 - Prob. 94PCh. 7.13 - Helium gas is compressed from 90 kPa and 30C to...Ch. 7.13 - Five kg of air at 427C and 600 kPa are contained...Ch. 7.13 - Prob. 97PCh. 7.13 - The well-insulated container shown in Fig. P 795E...Ch. 7.13 - Prob. 99PCh. 7.13 - Prob. 100PCh. 7.13 - It is well known that the power consumed by a...Ch. 7.13 - Prob. 102PCh. 7.13 - Prob. 103PCh. 7.13 - Saturated water vapor at 150C is compressed in a...Ch. 7.13 - Liquid water at 120 kPa enters a 7-kW pump where...Ch. 7.13 - Prob. 106PCh. 7.13 - Consider a steam power plant that operates between...Ch. 7.13 - Helium gas is compressed from 16 psia and 85F to...Ch. 7.13 - Nitrogen gas is compressed from 80 kPa and 27C to...Ch. 7.13 - Saturated refrigerant-134a vapor at 15 psia is...Ch. 7.13 - Describe the ideal process for an (a) adiabatic...Ch. 7.13 - Is the isentropic process a suitable model for...Ch. 7.13 - On a T-s diagram, does the actual exit state...Ch. 7.13 - Steam at 100 psia and 650F is expanded...Ch. 7.13 - Prob. 117PCh. 7.13 - Combustion gases enter an adiabatic gas turbine at...Ch. 7.13 - Steam at 4 MPa and 350C is expanded in an...Ch. 7.13 - Prob. 120PCh. 7.13 - Prob. 122PCh. 7.13 - Prob. 123PCh. 7.13 - Refrigerant-134a enters an adiabatic compressor as...Ch. 7.13 - Prob. 126PCh. 7.13 - Argon gas enters an adiabatic compressor at 14...Ch. 7.13 - Air enters an adiabatic nozzle at 45 psia and 940F...Ch. 7.13 - Prob. 130PCh. 7.13 - An adiabatic diffuser at the inlet of a jet engine...Ch. 7.13 - Hot combustion gases enter the nozzle of a...Ch. 7.13 - Refrigerant-134a is expanded adiabatically from...Ch. 7.13 - Oxygen enters an insulated 12-cm-diameter pipe...Ch. 7.13 - Prob. 135PCh. 7.13 - Prob. 136PCh. 7.13 - Steam enters an adiabatic turbine steadily at 7...Ch. 7.13 - 7–138 In an ice-making plant, water at 0°C is...Ch. 7.13 - Water at 20 psia and 50F enters a mixing chamber...Ch. 7.13 - Prob. 140PCh. 7.13 - Prob. 141PCh. 7.13 - Prob. 142PCh. 7.13 - Prob. 143PCh. 7.13 - In a dairy plant, milk at 4C is pasteurized...Ch. 7.13 - An ordinary egg can be approximated as a...Ch. 7.13 - Prob. 146PCh. 7.13 - Prob. 147PCh. 7.13 - In a production facility, 1.2-in-thick, 2-ft 2-ft...Ch. 7.13 - Prob. 149PCh. 7.13 - Prob. 150PCh. 7.13 - A frictionless pistoncylinder device contains...Ch. 7.13 - Prob. 152PCh. 7.13 - Prob. 153PCh. 7.13 - Prob. 154PCh. 7.13 - Prob. 155PCh. 7.13 - Liquid water at 200 kPa and 15C is heated in a...Ch. 7.13 - Prob. 157PCh. 7.13 - Prob. 158PCh. 7.13 - Prob. 159PCh. 7.13 - Prob. 160PCh. 7.13 - Prob. 161PCh. 7.13 - Prob. 162PCh. 7.13 - Prob. 163PCh. 7.13 - Prob. 164PCh. 7.13 - Prob. 165PCh. 7.13 - The space heating of a facility is accomplished by...Ch. 7.13 - Prob. 167PCh. 7.13 - Prob. 168PCh. 7.13 - Prob. 169RPCh. 7.13 - A refrigerator with a coefficient of performance...Ch. 7.13 - Prob. 171RPCh. 7.13 - Prob. 172RPCh. 7.13 - Prob. 173RPCh. 7.13 - A 100-lbm block of a solid material whose specific...Ch. 7.13 - Prob. 175RPCh. 7.13 - Prob. 176RPCh. 7.13 - A pistoncylinder device initially contains 15 ft3...Ch. 7.13 - Prob. 178RPCh. 7.13 - A 0.8-m3 rigid tank contains carbon dioxide (CO2)...Ch. 7.13 - Helium gas is throttled steadily from 400 kPa and...Ch. 7.13 - Air enters the evaporator section of a window air...Ch. 7.13 - Refrigerant-134a enters a compressor as a...Ch. 7.13 - Prob. 183RPCh. 7.13 - Three kg of helium gas at 100 kPa and 27C are...Ch. 7.13 - Prob. 185RPCh. 7.13 -
7–186 You are to expand a gas adiabatically from...Ch. 7.13 - Prob. 187RPCh. 7.13 - Determine the work input and entropy generation...Ch. 7.13 - Prob. 189RPCh. 7.13 - Prob. 190RPCh. 7.13 - Air enters a two-stage compressor at 100 kPa and...Ch. 7.13 - Steam at 6 MPa and 500C enters a two-stage...Ch. 7.13 - Prob. 193RPCh. 7.13 - Prob. 194RPCh. 7.13 - Prob. 196RPCh. 7.13 - Prob. 197RPCh. 7.13 - 7–198 To control the power output of an isentropic...Ch. 7.13 - Prob. 199RPCh. 7.13 - Prob. 200RPCh. 7.13 - A 5-ft3 rigid tank initially contains...Ch. 7.13 - Prob. 202RPCh. 7.13 - Prob. 203RPCh. 7.13 - Prob. 204RPCh. 7.13 - Prob. 205RPCh. 7.13 - Prob. 206RPCh. 7.13 - Prob. 207RPCh. 7.13 - Prob. 208RPCh. 7.13 - (a) Water flows through a shower head steadily at...Ch. 7.13 - Prob. 211RPCh. 7.13 - Prob. 212RPCh. 7.13 - Prob. 213RPCh. 7.13 - Consider the turbocharger of an internal...Ch. 7.13 - Prob. 215RPCh. 7.13 - Prob. 216RPCh. 7.13 - Prob. 217RPCh. 7.13 - Consider two bodies of identical mass m and...Ch. 7.13 - Prob. 220RPCh. 7.13 - Prob. 222RPCh. 7.13 - Prob. 224RPCh. 7.13 - The polytropic or small stage efficiency of a...Ch. 7.13 - Steam is compressed from 6 MPa and 300C to 10 MPa...Ch. 7.13 - An apple with a mass of 0.12 kg and average...Ch. 7.13 - A pistoncylinder device contains 5 kg of saturated...Ch. 7.13 - Prob. 229FEPCh. 7.13 - Prob. 230FEPCh. 7.13 - A unit mass of a substance undergoes an...Ch. 7.13 - A unit mass of an ideal gas at temperature T...Ch. 7.13 - Prob. 233FEPCh. 7.13 - Prob. 234FEPCh. 7.13 - Air is compressed steadily and adiabatically from...Ch. 7.13 - Argon gas expands in an adiabatic turbine steadily...Ch. 7.13 - Water enters a pump steadily at 100 kPa at a rate...Ch. 7.13 - Air is to be compressed steadily and...Ch. 7.13 - Helium gas enters an adiabatic nozzle steadily at...Ch. 7.13 - Combustion gases with a specific heat ratio of 1.3...Ch. 7.13 - Steam enters an adiabatic turbine steadily at 400C...Ch. 7.13 - Liquid water enters an adiabatic piping system at...Ch. 7.13 - Prob. 243FEPCh. 7.13 - Steam enters an adiabatic turbine at 8 MPa and...Ch. 7.13 - Helium gas is compressed steadily from 90 kPa and...
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
- Steam enters an adiabatic turbine at a given 9,200 kpa and the temperature is 475 degree celsius with a mass flow rate of 87 kg/s. The surrounding temperature is 300 kelvin. The effeiciency of the turbin is also said to be 0.75. With this given data, what would be the entropy generation rate, value of ideal work, and value of the lost work? note: steam is superheated.arrow_forwardIn an internal combustion engine, 2/3 of the heat supply takes place at constant volume and 1/3 at constant pressure. The other three condition changes of the engine are two isotropes and one isochore. The compression ratio (Va / Vb) is 10 and the cycle's highest and lowest pressures are 45 bar and 0.9 bar respectively. Work medium is an ideal gas with k = 1.35. All state changes are reversible. Calculate the thermal efficiency. gicd T4 d. qibc e Ec Ec e a S Varrow_forwardFor a refrigeration cycle using refrigerant 134a and a compressor isentropic efficiency of 80% and a mass flow rate of 0.2 kg/s, determine the coefficient of performance and the rate of entropy generation in the compressor. The state before the compressor is saturated vapor at 260 K; the temperature and the pressure at the condenser outlet are 305 K and 10 bar.arrow_forward
- Refrigerant 134a enters an air-cooled condenser at 12 bars and 60°C, and leaves as a saturated liquid at 12 bars. Atmospheric air at 35°C is blown over the condenser tubes and leaves at 45°C. The heat transfer between the two flfluid streams equals 25 MJ/h. Changes in kinetic and potential energy are negligible. Make any reasonable assumptions if necessary. Determine (a) the mass flow rates for the R-134a and the air, in kg/h, Hint: Use the energy conservation on each of the ⁅ uid streams separately. (b) the entropy production rate in the condenser, in kJ h-1K-1, Hint: Use the entropy balance over the whole condenser. (c) the change in kinetic energy for R-134a if the pipe diameter is 2.0 cm, in kJ/h (d) Draw the T-s diagram for the process for R-134a.arrow_forward1.A piston-cylinder device contains air at 427 degrees and 134kPa. A pressure increase of 1.378kPa was recorded after the air was compressed isentropically with minimum work input of 1.422KJ. Assuming air has constant specific heats evaluated at given temperature. Determine the mass of air in the device. 2. Air is used as the working fluid in a simple ideal brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300k, and a turbine inlet temperature of 1000k. Determine the required mass flow rate in (kg/s) of air for a net power output of 70MW, assuming both the compressor and the turbine have an isentropic efficiency of 100%. Assume constant specific heats at room temperaturearrow_forward1. In a constant temperature closed system process, 100 Btu of heat is transferred to the working fluid at 100 °F. What is the change of entropy of the working fluid?arrow_forward
- Consider an air-breathing Brayton cycle gas turbine. The compressor inlet state of the air is 302 K and 105 kPa, while the turbine inlet state is 962 Kand 1,42 MPa, What is the back work ratio for this device. expressed as a percentage to 1 decimal place? Take the specific heat c, of air to be 1.005 kJ-kgK and its specific heat ratio to be 1.4.arrow_forwardThe Brayton cycle, or one gas turbine cycle, operates between 1 bar and 300 K and 5 bar and 1000 K. Air is sucked into a double-acting compressor with cooling between the compression stages and, likewise, expansion. The turbine takes place in two stages with heating. complete during the expansion stage, calculate (a) Appropriate pressure between compression and expansion stages (bar) (b) net export work and (c) the ratio of work to drive the compressor to the work from the turbinearrow_forward1. The working substance for a Carnot cycle is 8 lb of air. The volume at the beginning of isothermal expansion is 9 cu ft and the pressure is 300 psia. The ratio of expansion during the addition of heat is 2 and the temperature of the cold body is 90°F. Find (a) Q, (b) Qg, (c) Va, (d) p, (e) V,, (f) p,, (g) p, (h) the ratio of expansion during the isentropic process, and (i) the overall ratio of compression. Ans. (a) 346.4 Btu; (b) -209.1 Btu; (c) 63.57 cu ft; (d) 25.64 psia; (e)31.79 cu ft; (f) 51.28 psia; (g) 13.59 psia; (h) 3.53; (8) 7.06arrow_forward
- A carnot cycle is conducted using air contained in a cylinder -piston configuration. Initially, the system contains air at 25 degC, 100 kPa and 0.01 m3. You may designate this as state 1. The system is first compressed isothermally until the volume is 0.002m3. From that point, the system undergoes a polytropic compression process with exponent y=1.4 until the volume further reduces to 0.001m3. After that the system undergoes an isothermal expansion process afterwhich, the system is subjected to an adiabatic expansion process until the system reaches the initial state completing a cycle.Determine the maximum P and T in the cycle, the net work of the cycle, heat input, heat rejected, the cycle efficiency (in %) and the mean effective pressure.arrow_forwardC. In an ideal gas turbine power device, the pressure ratio is 6, the temperature entering the compressor is 27°C, and the maximum allowable temperature of the turbine is 816°C. What is the efficiency of this power device when it is carried out in reversible operation? However, the specific ratio is 1.4. (a)20% (b)30% (c)40% (d)50%arrow_forwardA turboprop engine consists of a diffuser, compressor, combustor, turbine, and nozzle. The turbine drives a propeller as well as the compressor. Air enters the diffuser with a volumetric flow rate of 83.7 m3/s at 40 kPa, 240 K, and a velocity of 180 m/s, and decelerates essentially to zero velocity. The compressor pressure ratio is 10 and the compressor has an isentropic efficiency of 85 %. The turbine inlet temperature is 1,140 K, and its isentropic efficiency is 85 %. The turbine exit pressure is 50 kPa. Flow through the diffuser and nozzle is isentropic. Sketch the process on the T-s diagram and using an air-standard analysis, determine, the power delivered to the propeller, in MWt the velocity at the nozzle exit, in m/s. Neglect kinetic energy except at the diffuser inlet and the nozzle exit.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 Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering 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
Thermodynamic Availability, What is?; Author: MechanicaLEi;https://www.youtube.com/watch?v=-04oxjgS99w;License: Standard Youtube License