Physics Help! Calculate work done along a path using a PV diagram?

Question

A gas expands from I to F along the three paths indicated in http://www.webassign.net/sercp/p12-5.gif

Calculate the work done on the gas along each path
(a) IAF
I know this one is -810.4

(b) IF
I dont know how to find this one!

(c) IBF
I know this one is -202.6

Answer 1

(a) I ==> A: constant pressure process, work done = P*(v2-v1)= 8 atm*L = 810.5 J.
A ==> F: constant volume process.
Hence IAF: work done = 810.5J.
It must be positive, since the volume increases.

(b) First write pressure P as a function of volume v:
P(v) = 7.0 - 1.5v
Hence the work done = [integral](v: 2 to 4) Pdv
= [7v -(3/4)v^2] (evaluate from 2 to 4)
= (28-12) - (14-3) = 5 (atm*L)
= 506.6 J

(c) Similar to (a):
Work done = 2 atm*L = 202.6 J

A much simpler way is to consider the area underneath the curve. In this way:
(a) 4*(4-2) = 8 (atm*L)
(b) (4-2)*(4-1)/2 + 1*(4-2) = 3+2 = 5 (atm*L)
(c) 1*(4-2) = 2 (atm*L)