Air as an ideal gas executes a Carnot power cycle (T-s and p-v diagrams are give

Question

Air as an ideal gas executes a Carnot power cycle (T-s and p-v diagrams are given below) in a closed system. The maximum pressure in the cycle is 1300 kPa while the maximum temperature is 950 K. If the entropy increase during the isothermal expansion process is 0.25 kJ/kg.K and the net work output is 100 kJ/kg Please determine (a) The minimum temperature in the cycle, in K (5 points). Ob The pressure of state 4, in kPa (5 points) (c) The minimum pressure in the cycle, in kPa (10 points). (d) The heat input to the cycle, in kJ/kg (5 points). Ge) The thermal efficiency of the cycle (5 points) Assume the air has a constant specific heat ratio k 1.4. The molar mass of the air is 28.97 kg/kmol, and the universal gas constant is 8.314 kJ/kmol K.

Explanation / Answer

a) W = deltaT * delta S

100 kJ/kg = (950 - Tc) * (0.25 kJ/kgK)

400 = 950 - Tc

Tc = 550 K = 277 ºC

b) T1/T4 = (P1/P4)k-1/k

950/550 = (1300/P4).2857

P4 = 191.93 kPa

c) P = density * R * T / M

P = [0.706 kg/m3 * 8.31 m3Pa/Kmol * 550 K] / .02897 kg/kmol

P = 111.38 kPa

d) Qh = Th (deltaS)

Qh = 950K * 0.25 kJ/kgK

Qh = 237.5 kJ/kg

e) Efficiency = W/Qh = 100 kJ/kg/237 kJ/kg = 42.1 %

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