Archived Adiabatic expansion in a steady flow question

[wilkie610]

I an working on a problem in the text "Mechanics and Thermodynamics of Propulsion" 2e. The problem states a perfect gas with molecular weight M=20 and a specific heat ratio of Y=1.2 expands adiabatically in steady flow from a pressure of 6MPa, a temperature of 3000K, and a velocity of 200 m/s to a final pressure of 0.101 MPa. If the final temperature is 1800K and the final velocity is negligible, what is the work done

I know that adiabatic means no heat in or out of the system so dq=0
Y=cp/cv and cp=cv+R
dq=de+dw

My attempt:
First i find R=8314.3/20=415.715
then i find cv by cv=R/(Y-1) cv=2078.58
thus dw= (-de) where de=cv(T2-T1)
my answer for the work done is 2494.29 kJ/kg however the books answer is 3013 Kj/kj

what am i doing wrong?
thanks for your help

 

[Junyong]

dw = m*[(e2-e1)+(p2/rho2 - p1/rho1)+(v2^2 / 2 - v1^2 / 2)]
so, v2 = 0 , p/rho = RT(p=rho*R*T)
and Cp=Cv+R finally dw = CP(T2-T1) - v1^2 / 2

you do not think V1 ok?

 

[Chestermiller]

dw = m*[(e2-e1)+(p2/rho2 - p1/rho1)+(v2^2 / 2 - v1^2 / 2)]
so, v2 = 0 , p/rho = RT(p=rho*R*T)
and Cp=Cv+R finally dw = CP(T2-T1) - v1^2 / 2

you do not think V1 ok?

This looks correct to me. Nice job of applying the open system version of the 1st law.