Engineering, 27.02.2020 05:01 veheca

Determine the percent error in using the ideal gas model to determine the specific volume of (a) water vapor at 4000 lbf/in.2, 10008F. (b) water vapor at 5 lbf/in.2, 2508F. (c) ammonia at 40 lbf/in.2, 608F. (d) air at 1 atm, 5608R. (e) Refrigerant 134a at 300 lbf/in.2, 1808F.

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Answer from: Ilikepandas2019

a) 24.01%

b) 0.35%

c) 3.43%

d) 0%

e) 37.31%

Explanation:

A) water vapor=> H2O

From table @4000 lbf/in^2, 1000°F v = 0.1752 ft^3/ib

m = 18.02 ib/ibmol

P = 4000 lbf/in^2

From the ideal gas model

PV/m = mRT/m

V = RT/Pm

Where R = 1945 (ft.ibf)/(ibmol.°R)

T = 1000°F = 1459.67°R

Therefore

V = (1945 × 1459.67) ÷ (4000 × 18.02) = 2255190.19 ÷ 72080 = 0.21727 ft^3/ib

Error =( V - v)/v × 100% = (0.21727 - 0.1752) ÷ 0.1752 = 0.2401 ×100% = 24.01%

B) water vapor=> H2O

From table @ 5 lbf/in^2, 250°F v = 84.21 ft^3/ib

m = 18.02 ib/ibmol

P = 5 lbf/in^2

From the ideal gas model

PV/m = mRT/m

V = RT/Pm

Where R = 1945 (ft.ibf)/(ibmol.°R)

T = 250°F = 709.67°R

Therefore

V = (1945 × 709.67) ÷ (5 × 18.02) =84.51 ft^3/ib

Error =( V - v)/v × 100% = (84.51 - 84.21) ÷ 84.21 = 0.003538 ×100% = 0.35%

C) ammonia =>

From table @40 lbf/in^2, 60°F v = 7.9134 ft^3/ib

m = 17.03 ib/ibmol

P = 40 lbf/in^2

From the ideal gas model

PV/m = mRT/m

V = RT/Pm

Where R = 1945 (ft.ibf)/(ibmol.°R)

T = 60°F = 519.67°R

Therefore

V = (1945 × 519.67) ÷ (40 × 17.03) = 8.189 ft^3/ib

Error =( V - v)/v × 100% = (8.189 - 7.9134) ÷ 7.9134 = 0.03432 ×100% = 3.43%

D) Air at 1 atm =>

No table so we assume air is ideal

m = 28.97 ib/ibmol

P = 14.71 lbf/in^2

From the ideal gas model

PV/m = mRT/m

V = RT/Pm

Where R = 1945 (ft.ibf)/(ibmol.°R)

T = 560°R

Therefore

V = (1945 × 560) ÷ (14.71 × 28.97) = 14.099 ft^3/ib

Since Air is ideal error is zero =0%

E) refrigerant =>

From table @300 lbf/in^2, 180°F v = 0.1633 ft^3/ib

m = 102.03 ib/ibmol

P = 300 lbf/in^2

From the ideal gas model

PV/m = mRT/m

V = RT/Pm

Where R = 1945 (ft.ibf)/(ibmol.°R)

T = 180°F = 639.67°R

Therefore

V = (1945 × 639.67) ÷ (300 × 102.03) = 0.22422 ft^3/ib

Error =( V - v)/v × 100% = (0.22422 - 0.1633) ÷ 0.1633 = 0.37306 ×100% = 37.31%

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