Problem 17.47

17.47. a)
The work done during each segment is equal to the area under each part of the PV curve.
W = W_DA + W_AB + W_BC + W_CD
W = P₀(V₀-3V₀) + 0 + 3P₀(3V₀-V₀) + 0
W = 4P₀V₀

b)
Since the initial and final values of the temperature of the system are equal, then $\Delta U = 0$. It then follows that Q = W, so
Q = W = 4P₀V₀

c)
Since P₀V₀ = nRT₀, then the work equals,
W = 4P₀V₀ = 4nRT₀
W = 4(1)(8.31)(273)
$W = 9.08 \times 10^{3} J$