a. Since PA = PB and VA/TA = VB/TB giving TB = T2 = T1/2
b. CA is an isotherm so TA = TC so PAVA = PCVC; P1V1 = P2(V1/2) giving P2 = 2P1
c. Work is the area under the line. No work is done from B to C so we just need the area under line AB.
Specifically, W = –P∆V = –P1(V1/2 – V1) = +½P1V
d. Heat was added in processes BC and CA, but not in AB.
BC: W = 0 so ∆U = Q and temperature rises so ∆U is positive
CA: ∆U = 0 (isotherm) so Q = –W and it is an expansion so W is negative and therefore Q is positive
AB: Compression so W is + and temperature drops so ∆U is negative and Q = ∆U – W which must be negative