One pound mass of air as an ideal gas executes a Carnot power cycle. The isother
ID: 1817157 • Letter: O
Question
One pound mass of air as an ideal gas executes a Carnot power cycle. The isothermal expansion occurs at 2050 degrees R from a pressure of 2700 psi to a pressure of 1885 psi. The isothermal compression occurs at 535 degrees R from a pressure of 14.7 psi to a pressure of 22.5 psi. Determine the:
a.) Heat transfer to the air during the isothermal expansion in (BTU)
b.) Heat transfer from the air during the isothermal compression (BTU)
c.) Work done by, or on, the air during each of the four processes (BTU)
d.) Cycle thermal efficiency
Explanation / Answer
mass m = 1 lbm, T1 = 2050 R, p1 = 2700 psi, p2 = 1885 psi.
T2 = 535 R, p3 = 14.7 psi, p4 = 22.5 psi.
R = 0.06855 Btu/lbm.R, Cv = 0.171 Btu/lbm.R
a.) Heat transfer to the air during the isothermal expansion in (BTU)
Q1 = mRT1ln(p1/p2) = 50.49 Btu
b.) Heat transfer from the air during the isothermal compression (BTU)
Q2 = mRT2ln(p4/p3) = 15.61 Btu
c.) Work done by, or on, the air during each of the four processes (BTU)
during the isothermal expansion: work = Q1 = mRT1ln(p1/p2) = 50.49 Btu (by the air)
during the adiabatic expansion: work = m*Cv*(T1 - T2) = 259.1 Btu (by the air)
during the isothermal compressionwork = Q2 = mRT2ln(p4/p3) = 15.61 Btu (on the air)
during the adiabatic compression: work = m*Cv*(T1 - T2) = 259.1 Btu (on the air)
d.) Cycle thermal efficiency = 1 - Q2/Q1 = 69.1%
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