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//(12.4) A gas mixture consisting of CO2 and O2 with mole fractions 0.8 and 0.2, respectively, expands isentropically and at steady state through a nozzle from 700 K, 5 bars, 3 m/s to an exit pressure of 1 bar. Determine (a) the temperature at the nozzle exit, in K, (b) the entropy changes of the CO2 and O2 from inlet to exit, in KJ/Kmol.K (c) the exit velocity, in m/s.
//solution
//variable initialization
y1 = .8 //mole fraction of CO2
y2 = .2 //mole fraction of O2
T1 = 700 //in kelvin
p1 = 5 //in bars
V1 = 3 //in m/s
p2 = 1 //in bars
//part(a)
//from table A-23
sO2barT1 = 231.358
sCO2barT1 = 250.663
RHS = y2*sO2barT1 + y1*sCO2barT1 + 8.314*log(p2/p1)
//using table A-23
LHSat510K = y2*221.206 + y1*235.7
LHSat520K = y2*221.812 + y1*236.575
//using linear interpolation,
T2 = 510 +[(520-510)/(LHSat520K-LHSat510K)]*(RHS-LHSat510K)
printf('the temperature at the nozzle exit in K is: %f',T2)
//part(b)
//from table A-23
sbarO2T2 = 221.667 //in kj/kmol.K
sbarO2T1 = 231.358 //in kj/kmol.K
sbarCO2T2 = 236.365 //in kj/kmol.K
sbarCO2T1 = 250.663 //in kj/kmol.K
deltasbarO2 = sbarO2T2-sbarO2T1-8.314*log(p2/p1) //in kj/kmol.K
deltasbarCO2 = sbarCO2T2-sbarCO2T1-8.314*log(p2/p1) //in kj/kmol.K
printf('\n\nthe entropy changes of the CO2 from inlet to exit, in KJ/Kmol.K is: %f',deltasbarCO2)
printf('\nthe entropy change of the O2 from inlet to the exit in kj/kmol.k is: %f',deltasbarO2)
//part(c)
//from table A-23, the molar specific enthalpies of O2 and CO2 are
h1barO2 = 21184
h2barO2 = 15320
h1barCO2 = 27125
h2barCO2 = 18468
M = y1*44 + y2*32 //apparent molecular weight of the mixture in kg/kmol
deltah = (1/M)*[y2*(h1barO2-h2barO2) + y1*(h1barCO2-h2barCO2)]
V2 = sqrt(V1^2+ 2*deltah*10^3)
printf('\n\nthe exit velocity in m/s is: %f',V2)
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