Adiabatic expansion in a steady flow question

In summary, the problem states that 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. The final temperature is 1800K and the final velocity is negligible. The question is asking for the work done, which can be calculated using the open system version of the first law of thermodynamics. The final answer should be 3013 kJ/kg, but the calculated answer is only 2494.29 kJ/kg. The error may be due to not considering the
  • #1
wilkie610
3
0
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
 
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  • #2
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?
 
  • #3
Junyong said:
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.
 

What is adiabatic expansion in a steady flow?

Adiabatic expansion in a steady flow is a thermodynamic process in which a fluid expands without any heat transfer or exchange with its surroundings. This means that the temperature of the fluid remains constant during the expansion.

What are some examples of adiabatic expansion in a steady flow?

Some examples of adiabatic expansion in a steady flow include the expansion of air in a jet engine, the expansion of gas in a compressor, and the expansion of steam in a turbine.

How does adiabatic expansion in a steady flow differ from isothermal expansion?

The main difference between adiabatic expansion in a steady flow and isothermal expansion is that adiabatic expansion occurs without any heat transfer, while isothermal expansion occurs at a constant temperature with heat transfer.

What is the equation for calculating adiabatic expansion in a steady flow?

The equation for adiabatic expansion in a steady flow is P1V1^gamma = P2V2^gamma, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and gamma is the adiabatic constant.

What are the applications of adiabatic expansion in a steady flow?

Adiabatic expansion in a steady flow has many applications in engineering and physics, including in the design of gas turbines, compressors, and heat engines. It is also used in the study of atmospheric processes, such as the expansion of air in weather systems.

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