Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 3.8, Problem 120RP
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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Answer to Problem 120RP

The volume change using compressibility factor is 0.07006m3_.

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

Explanation of Solution

Refer to Table A-1, obtain the gas constant, critical pressure, and critical temperature of steam.

R=0.4615kPam3kgK

Tcr=647.1K

Pcr=22.06MPa

Refer to Table A-6, obtain the specific volume 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 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) (I)

Here, mass of steam is m.

Write the equation of reduced pressure at inlet condition.

PR1=P1Pcr (II)

Here, critical pressure of steam is Pcr and inlet pressure of steam is P1.

Write the equation of reduced temperature at inlet condition.

TR1=T1Tcr (III)

Here, critical temperature of steam is Tcr and inlet temperature of steam is T1.

Write the equation of reduced pressure at outlet condition.

PR2=P2Pcr (IV)

Here, outlet pressure of steam is P2.

Write the equation of reduced temperature at outlet condition.

TR12=T2Tcr (V)

Here, outlet temperature of steam is T2.

Write the volume of piston cylinder device at inlet state.

ν1=Z1mRT1P1 (VI)

Here, the compressibility factor at inlet state is Z1 and gas constant is R.

Write the volume of piston cylinder device at outlet state.

ν2=Z2mRT2P2 (VII)

Here, the compressibility factor at outlet state is Z2.

Calculate the change in the volume using compressibility factor.

Δνchart=ν1ν2 (VIII)

Calculate the percentage of error involved.

Error=vexactvchartvchart×100% (IX)

Conclusion:

Substitute 0.2 kg for m, 1.31623m3/kg for v1, and 0.95986m3/kg for v2 in Equation (I).

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

Substitute 0.2 MPa for P1 and 22.06MPa for Pcr in Equation (II).

PR1=0.2MPa22.06MPa=0.0091

Substitute 300°C for T1 and 647.1 K for Tcr in Equation (III).

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

Substitute 0.2 MPa for P2 and 22.06MPa for Pcr in Equation (IV).

PR2=0.2MPa22.06MPa=0.0091

Substitute 150°C for T2 and 647.1 K for Tcr in Equation (V).

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.

Z2=0.9897

Substitute 0.9956 for Z1, 0.2 kg for m, 0.4615kPam3kgK for R, 300°C for T1, and 200 kPa for P1 in Equation (VI).

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

Substitute 0.9897 for Z2, 0.2 kg for m, 0.4615kPam3kgK for R, 150°C for T2, and 200 kPa for P2 in Equation (VII).

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

Substitute 0.2633m3 for ν1 and 0.1932m3 for ν2 in Equation (VIII).

Δνchart=0.2633m30.1932m3=0.07006m3

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

Substitute 0.07006m3 for Δνchart and 0.07128m3 for Δνexact in Equation (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 3 Solutions

Thermodynamics: An Engineering Approach

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