A gas is compressed in a pistonandcylinder 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 quasiequilibrium 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 
P_{avg} (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 


W_{total} 
331.8 
J 












Verify: 
None of the
assumptions can be verified from the data given in the problem statement. 










Answers : 
W_{total} 
332 
J 







































