# Example Problem with Complete Solution

4A-5 : Quasi-Equilibrium Expansion of a Gas 4 pts
A gas is compressed in a piston-and-cylinder device from 100 kPa to 700 kPa. Estimate the boundary work done by the gas during the process. The following measurements were made during the process. Read : The key concept here is that boundary or PV work is represented by the area under the process path curve on a PV Diagram.  So, once we plot the given data on a PV Diagram, all we need to do is numerically integrate to determine the area under the curve and we will have the work !
Diagram: Given: P (kPa) V (L) Find: W ??? J
100 1.025
200 0.900
300 0.793
400 0.651
500 0.517
600 0.375
700 0.224
Assumptions: 1 - Each state in the data table is an equilibrium state.
2 - The process is a quasi-equilibrium process.
3 - The system is a closed system.
4 - The trapezoidal rule gives an acceptable estimate of the area under the process path in the PV Diagram.
Equations / Data / Solve:
The area of each trapezoid under the process path in the PV Diagram is the product of the average pressure for that trapezoid and the change in volume across the trapezoid. Eqn 1
Where  subscript a refers to the left side of each trapezoid and subscript b refers to the right side of each trapezoid in the PV Diagram.
Trapezoid Pavg (kPa) DV (L) W (J)
A 650 -0.151 -98
B 550 -0.142 -78
C 450 -0.134 -60
D 350 -0.142 -50
E 250 -0.107 -27
F 150 -0.125 -19 Wtotal -331.8 J
Verify: None of the assumptions can be verified from the data given in the problem statement. 