(1) An insulated piston-cylinder device initially contains 8.573 kg of air at 20

Question

(1) An insulated piston-cylinder device initially contains 8.573 kg of air at 20 psia and 60ºF. Then 1000 Btu per lb of air of heat is added to the system while the pressure remains constant. Determine the change in entropy of the air using a variable heat capacity in units of Btu/R. (ANS: 4.726)

(2) Air enters an adiabatic turbine at 493ºC and 1.9 MPa and leaves at 51 kPa. If the isentropic efficiency of the turbine is 91%, what is the actual exhaust temperature at the outlet in ºC? Assume a constant heat capacity. (ANS: 43.90)

I know the answer, just want to know how to get this answer.

Explanation / Answer

For isentropic expansion,

T2_is / T1 = (P2 / P1)^((k1-)/k)

T2_is / (493+273) = (51*10^3 / 1.9*10^6)^((1.4-1)/1.4)

T2_is = 272.5 K = 0 deg C

Efficiency = (T2_is - T1) / (T2 - T1)

0.91 = (T2 - 493) / (0 - 493)

T2 = 44.4 deg C

Q - W = (u2 - u1)

1000 - R*(T2 - T1) = Cv*(T2 - T1)

1000 = (Cv + R)*(T2 - T1)

1000 = Cp*(T2 - T1)

1000 = (h2 - h1)

h2 - h1 = 1000

From air properties at, 20 psi and 60 F, we have h1 = 124 Btu / lb and s1 = 1.61 Btu / lb-R

h2 = 1000 + h1 = 1124 Btu/lb

From air properties at P2 = P1 = 20 psi and h2 = 1124 Btu/lb, we get s2 = 2.16 Btu / lb-R

Entropy change = m*(s2 - s1)

= 8.573*(2.16 - 1.61) = 4.7 Btu/R

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