Model the ideal gas as having variable specific heats, and comput the thermal ef

Question

Model the ideal gas as having variable specific heats, and comput the thermal efficiency of the cycle without using m=1-Th/Tl.

Air in a closed system executes the Carnot cycle. The minimum and maximum temperatures are T3=T4=Tl=300K abd T1=T2=Th=900K. The minimum and maximum pressures are P3=20kPa and P1=2000kPa. The mass of the air in the system is 0.003kg. Model the air as an ideal gas having VARIABLE specific heats, using values from the tables.

Find pressures P2 and P4. (ans: 1086.44kPa and 38.8176kPa)

please do not answer using formulas for constant specific heats. This is a variable specific heat question.

Explanation / Answer

at T3 = T4

Pr3 = Pr4 = 1.39 (From Air properties table)

at T1 = T2 ,

Pr1 = Pr2 = 75.29 (From Air properties table)

Pr4/Pr1 = P4/P1

1.39/75.29 = P4/2000

P4 = 36.92 kPa (due to data variation in properties table there is slight difference in answer)

Pr3/Pr2 = P3/P2

1.39/75.29 = 20/P2

P2 = 1083.31 kpa   (due to data variation in properties table there is slight difference in answer)

Thermal efficiency = 1 -300/900

= 66.67%

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