calculate the amount of work done on the system from 0-2 and then for the entire curve from 0-5 given the volume and pressure.

Question

a pressure versus volume diagram for a system is shown in the figure. the values for the points in the diagram are shown in the table (couldn't include the image. points 0,1,2 make a triangular region. points 2,3,4 make a rectangular region. points 4,5 make a triangular region. if that helps)

calculate the amount of work done on the system from 0-2 and then for the entire curve from 0-5 given the volume and pressure. 

volume: pressure: 

v0 = 25.4 p0 = 1.37 x 10^4

v1 = 19.3 p1 = 1.37 x 10^4

v2 = 16.8 p2 = 5.76 x 10^3

v3 = 13.9 p3 = 5.76 x 10^3

v4 = 13.9 p4 = 2.78 x 10^3

v5 = 8.36 p5 = 1.57 x 10^3

Answer 1

Hi Lily,

There are 4 regions (4processes) here

0 to 1: isobaric W=Po(V1-Vo)

1 to 2: (process known by the P(V) linear so it forms a trapezoid with area (which is equal to work)

W=1/2(p1+p2)(V2-V1)

2 to 3 isobaric: W=P2(V3-V2)

3 to 4 isochoric: W=0

4 to 5 : again, a trapezoidal graph : W=1/2(p4+p5)(V4-V5)

Work from 0 to 2 is the sum of works from 0 to1 & from 1 to 2. In a similar way you'd find the work on the rest of the path (2 to 5) and therefore on the whole path 0 to 5

Hope it'd help

Best

Dr.Ariel B.