Thermal efficiency of the cycle 1kg of Propane in a piston c

Thermal efficiency of the cycle. 1kg of Propane in a piston cylinder assembly undergoes the process described by the figure below. Note that there is heat transfer between the assembly and its surroundings which is at a temperature of T_b. During the process, the work done by the propane is measured as 42.4 kJ. Neglecting the effects of potential and kinetic energy, determine if the value of the work measured is correct or not. Two inventors present the same insulated turbine with inlet and exit conditions described in figure below. One claims that the work turbine is 606 kJ/kg, while the second claims a 765.9kJ/kg. Can either claim be correct? Please explain.

Solution

At State 1

P1 * V1 = m * R * T1

8 * 10^5 * V1   = 1 * 189 * 323

V1 = 0.076309 m^3

At State 2

P1 * V1 = m * R * T1

3 * 10^5 * V1   = 1 * 189 * 293

V1 = 0.18459 m^3

Change in internal Energy   = m * Cv * (20 - 50) = -1 * 1480 * 30 = -44.4 kJ

Q = U + W

W = Q - U   = Q + 44.4

For W = 42.4 kJ

Q   = - 2 kJ   which is not possible because gas is expanding and temperature is decreasing. Q has to be positive.

Therefore W = 42.4 kJ is not possible.