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During an experimental test, gas in a cylinder undergoes an expansion and moves a piston. Pressure and volume data taken during the test is given in the table below. Find the thermodynamic work performed by the gas in the cylinder in the process of expanding from a volume of 0.50 liters to 1.20 liters. Use all of the data in the table in calculating the work.Volume (liters)Pressure (kPa)0.5014000.6010900.708750.807250.906151.005601.105251.20500

Question

During an experimental test, gas in a cylinder undergoes an expansion and moves a piston. Pressure and volume data taken during the test is given in the table below. Find the thermodynamic work performed by the gas in the cylinder in the process of expanding from a volume of 0.50 liters to 1.20 liters. Use all of the data in the table in calculating the work.

Volume (liters) Pressure (kPa)
0.50 1400
0.60 1090
0.70 875
0.80 725
0.90 615
1.00 560
1.10 525
1.20 500
check_circleAnswer
Step 1

The gas in the cylinder expands and this expansion results in movement of the piston. The work is done by the gas on the system hence the expansion process will result in negative work.

From the given data, the curve fitting equation is to be determined. The curve fitting equation comes out to be

1600
1400
1200
PvL23-577.61
1000
800
600
400
200
0.2
0.4
0.6
0.8
1
1.2
1.4
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1600 1400 1200 PvL23-577.61 1000 800 600 400 200 0.2 0.4 0.6 0.8 1 1.2 1.4

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Step 2

The curve fitting equation suggests that the process is polytropic where the ratio of specific heats has the value of 1.213 and the constant has the value of 577.61

The work done by the gas on the piston can be calculated as

W -Jpdv
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W -Jpdv

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Step 3

Integrating the equation obtained from the curve fitting...

Here, the equation from the pressure volume data comes out as pV1213 =577.61
Putting the value of P in the formula of work
1.20
577.61
.dV
v1213
W
0.50
1500
1000
500
0.6
0.8
10
1.2
W 534.726 kJ(Negative
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Here, the equation from the pressure volume data comes out as pV1213 =577.61 Putting the value of P in the formula of work 1.20 577.61 .dV v1213 W 0.50 1500 1000 500 0.6 0.8 10 1.2 W 534.726 kJ(Negative

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