Problem 17.30

17.30. a)
For IAF,
W_IAF = W_IA + W_AF  =  0 + (1.5)(.05)
W_IAF = .75 L atm  =  76.0 J
For IBF,
W_IBF = W_IB + W_BF  =  (2)(0.5) + 0
W_IBF = 1.0 L atm  =  101 J
For IF,
W_IF = area under the curve
$W_{IF} = \frac{1}{2} (.5)(.5) + (1.5)(.5)$
W_IF = .875 L atm  =  88.6 J

b)
The change in thermal energy of the system between the initial conditions at A and the final conditions at B is given by
$\Delta U = U_{f} - U_{i}$
$\Delta U = 182 J - 91 J ~=~ 91 J$
So, the net thermal energy in the process is given by:
For IAF,
$Q_{IAF} = \Delta U + W_{IAF}$
Q_IAF = 91 J + 76 J  =  167 J
For IBF,
$Q_{IBF} = \Delta U + W_{IBF}$
Q_IBF = 91 J + 101 J  =  192 J
For IF,
$Q_{IF} = \Delta U + W_{IF}$
Q_IF = 91 J + 89 J  =  180 J