A gas undergoes a thermodynamic cycle consisting of three processes: process 1-2: constant volume, v = 0.028 m3, u2 - u1 = 26.4 kj process 2-3: expansion with pv = constant, u3 = u2 process 3-1: constant pressure, p = 1.1 bar, w31 = - 10.5 kj there are no significant changes in kinetic or potential energy. (a) calculate the net work for the cycle, in kj. (b) calculate the heat transfer for process 2-3, in kj. (c) calculate the heat transfer for process 3-1, in kj. (d) is this a power cycle (depict 1) or a refrigeration cycle (depict 0) ?

Process 1-2: V1 = V2 = 0.028 m^3; U2 - U1 = 26.4 kJ

Process 2-3: PV = Constant; U3 = U2

Process 3-1: P3 = P1 = 1.1 Bar; W31 = - 10.5 kJ

Part (a) : Net work for the cycle

W = W12 + W23 + W31

W12 = 0 kJ (since volume is constant)

W23 = C*ln (v3/v2); but, W31 = P3 (V1-V3) = > V1-V3 = W31/P3 = - 10.5 / (1.1*10^5) = - 9.55*10^-5 = > V3 = V1+9.55*10^-5 = 0.0281 m^3

In addition, PV = C = P3V3 = 1.1*10^5*0.0281 = 3090.5

Then, W23 = 3090.5*ln (0.0281/0.028) = 11.02 kJ

Substituting;

W = 0+11.02-10.5 = 0.518 kJ

Part (b) : Heat transfer in process 2-3

Q23-W23 = U3-U2, but U3 = U2 and thus U3-U2 = 0

Then,

Q23 = W23 = 11.02 kJ

Part (c) : Heat transfer for process 3-1

Q31-W31 = U1-U3 = U1-U2 = - (U2-U1) = - 26.4

Q31 = - 26.4+W31 = - 26.4-10.5 = - 36.9 kJ

Part (d) : Power or refrigeration cycle?

Q_cycle = Q12 + Q23 + Q31 = 26.4+11.02-36.9 = 0.52 kJ

W_cycle = 0.52 kJ

Since, Q_cycle >0 and W_cycle > 0, this is a power cycle.