Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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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
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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%_.

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Chapter 4 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

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