Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 4, Problem 105RQ
To determine

The volume change using compressibility factor.

The error involved between the specific volume of actual value and specific volume using compressibility chart.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

The mass of steam (m) is 0.2 kg.

The initial pressure of the steam (P1) is 200 kPa.

The initial temperature of the steam (T1) is 300°C.

The final temperature of the steam (T2) is 150°C.

Calculation:

Refer to Table A-1, obtain the gas constant (R), critical pressure (Pcr), and critical temperature (Tcr) of steam.

  R=0.4615kPam3kgK

  Tcr=647.1K

  Pcr=22.06MPa

Refer to Table A-6, obtain the specific volume (v1) at inlet condition by reading the value of P and T1 of 200 kPa and 300°C.

  v1=1.31623m3/kg

Refer to Table A-6, obtain the specific volume at outlet (v2) condition by reading the value of P and T2 of 200 kPa and 150°C.

  v2=0.95986m3/kg

Calculate the change in the volume of the exat value.

  Δν=m(v1v2)Δν=0.2kg(1.31623m3/kg0.95986m3/kg)=0.07128m3

Calculate the  reduced pressure at inlet condition.

  PR1=P1PcrPR1=0.2MPa22.06MPa=0.0091

Write the equation of reduced temperature at inlet condition.

  TR1=T1Tcr

  TR1=300°C647.1K=(300+273)K647.1K=0.886

Refer to figure A-15, “The compressibility chart”, obtain the compressibility factor, Z1  by reading the calculated reduced pressure and reduced temperature at inlet state of 0.0091 and 0.886.

  Z1=0.9956

Write the equation of reduced pressure at outlet condition.

  PR2=P2Pcr

  PR2=0.2MPa22.06MPa=0.0091

Write the equation of reduced temperature at outlet condition.

  TR12=T2Tcr

  TR2=150°C647.1K=(150+273)K647.1K=0.65

Refer to figure A-15, “The compressibility chart”, obtain the compressibility factor (Z2), by reading the calculated reduced pressure and reduced temperature at inlet state of 0.0091 and 0.65.

The compressibility factor (Z2) is 0.9897.

Write the volume of piston cylinder device at inlet state.

  ν1=Z1mRT1P1

  ν1=(0.9956)(0.2kg)(0.4615kPam3kgK)(300°C)200kPa=(0.9956)(0.2kg)(0.4615kPam3kgK)(300+273)K200kPa=0.2633m3

Write the volume of piston cylinder device at outlet state.

  ν2=Z2mRT2P2

  ν2=(0.9897)(0.2kg)(0.4615kPam3kgK)(150°C)200kPa=(0.9897)(0.2kg)(0.4615kPam3kgK)(150+273)K200kPa=0.1932m3

Calculate the change in the volume using compressibility factor.

  Δνchart=ν1ν2

  Δνchart=0.2633m30.1932m3=0.07006m3

Thus, the volume change using compressibility factor is 0.07006m3_.

Calculate the percentage of error involved.

  Error=vexactvchartvchart×100%        (IX)

  Error=0.07128m30.07006m30.07006m3×100%=1.7%

Thus, the error involved between the volume change of actual value and volume change using compressibility chart is 1.7%_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 4 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Does hfg change with pressure? How? Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Which process requires more energy: completely...Ch. 4 - In the absence of compressed liquid tables, how is...Ch. 4 - In 1775, Dr. William Cullen made ice in Scotland...Ch. 4 - Complete this table for H2O: Ch. 4 - Prob. 21PCh. 4 - Complete this table for H2O: Ch. 4 - Prob. 24PCh. 4 - Prob. 26PCh. 4 - Complete this table for refrigerant-134a: Ch. 4 - A 1.8-m3 rigid tank contains steam at 220°C....Ch. 4 - Prob. 29PCh. 4 - R-134a, whose specific volume is 0.6243 ft3/lbm,...Ch. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Refrigerant-134a at 200 kPa and 25°C flows through...Ch. 4 - The average atmospheric pressure in Denver...Ch. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - One pound-mass of water fills a 2.4264-ft3...Ch. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Water initially at 200 kPa and 300°C is contained...Ch. 4 - Saturated steam coming off the turbine of a steam...Ch. 4 - Water in a 5-cm-deep pan is observed to boil at...Ch. 4 - A cooking pan whose inner diameter is 20 cm is...Ch. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - A piston–cylinder device contains 0.005 m3 of...Ch. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - A rigid vessel contains 8 kg of refrigerant-134a...Ch. 4 - Prob. 63PCh. 4 - A piston–cylinder device initially contains 50 L...Ch. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - The air in an automobile tire with a volume of...Ch. 4 - The air in an automobile tire with a volume of...Ch. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - What is the principle of corresponding states? Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - Prob. 84PCh. 4 - Prob. 85PCh. 4 - Prob. 86PCh. 4 - Prob. 87PCh. 4 - What is the percentage of error involved in...Ch. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Prob. 93RQCh. 4 - Prob. 94RQCh. 4 - A tank contains argon at 600°C and 200 kPa gage....Ch. 4 - Prob. 96RQCh. 4 - Prob. 97RQCh. 4 - Prob. 98RQCh. 4 - Prob. 99RQCh. 4 - Prob. 100RQCh. 4 - Prob. 101RQCh. 4 - Prob. 102RQCh. 4 - A 4-L rigid tank contains 2 kg of saturated...Ch. 4 - The gage pressure of an automobile tire is...Ch. 4 - Prob. 105RQCh. 4 - Prob. 106RQCh. 4 - Prob. 107RQCh. 4 - Prob. 108RQCh. 4 - Prob. 109RQCh. 4 - Prob. 110RQCh. 4 - Prob. 111RQCh. 4 - Prob. 112RQ
Knowledge Booster
Background pattern image
Mechanical Engineering
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.
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Thermodynamics - Chapter 3 - Pure substances; Author: Engineering Deciphered;https://www.youtube.com/watch?v=bTMQtj13yu8;License: Standard YouTube License, CC-BY