A pressure versus volume (pV) diagram is shown in the figure below for a system. The arrows of the curve indicate the direction of the process and the points of interest are labelled. Calculate the amount of work done on the system from 0 - 2 and then for the entire curve 0 - 5 . The values for the points in the diagram are:
Vo=25.8, V1= 19.9, V2=16.0, V3= 14.2, V4=14.2, V5= 7.85
P0=1.37E4, P1= 1.37E4, P2=5.76E3, P3= 5.76E3, P4=2.78E3, P5= 1.00E3
The work done on the system at each step is -p*delta-V.
Since every delta-V is negative, the work done on the system will come out positive.
From 0 to 1, it's (19.9-25.8 m^3)(13.7 kPa) = about 80.83 kJ
From 1 to 2, it's (16-19.9 m^3)(9.73 kPa) = about 37.95 kJ.
From 2 to 3, it's (14.2-16 m^3)(5.76 kPa) = about 10.37 kJ.
From 3 to 4, it's zero.
From 4 to 5, it's (7.85-14.2 m^3)(1.89 kPa) = about 12 kJ
[P for o 1 to 2 and for 4 to 5 are the average value of the initial and final P]
W(0 to 2) = 80.83+37.95 kJ = 118.78 kJ = 1.19 x 105 J
W(o to 5) = 80.83+37.95+10.37+0+12 = 141.15 kJ = 1.41 x 105 J
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