  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
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 help_outlineImage Transcriptionclose1600 1400 1200 PvL23-577.61 1000 800 600 400 200 0.2 0.4 0.6 0.8 1 1.2 1.4 fullscreen
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

Step 3

Integrating the equation obtained from the curve fitting... help_outlineImage TranscriptioncloseHere, 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 fullscreen

Want to see the full answer?

See Solution

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Mechanical Engineering 