# Adiabatic expansion of argon gas

#### Erik Horwath

argon enters a turbine at a rate of 800 kg/min, a temp of 800C and a pressure of 1.5MPa. It expands adiabatically as it pushes on the turbine blades and exits at a pressure 300KPa. Calculate its temperature at exit.

The equations I am working with are PV^(gamma)=constant and TV^(gamma-1)=constant. In this case gamma=1.67. If I could figure out how the second of these equations was derived from the first (I'm assuming it involves PV=nRT) I have a feeling I could solve the problem by deriving a similar expression involving P and T but I not sure how and my brain is tired.
:yuck:
Help would be appreciated. By the way I have the answer - it is 564K.

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#### Doc Al

Mentor
You have the right idea. Start with the first equation, PV^(gamma)=constant. Then pick the variable you would like to eliminate. To eliminate P, substitute P = nRT/V (from the ideal gas law). Just plug it in and you'll see that it equals your second equation, TV^(gamma-1)=constant. (The constants will be different of course, but that doesn't matter.) Try it!

Then to find the equation you need to solve your problem, eliminate V in the same manner.

#### quark

Your answer is ok if the above said pressures are absolute, otherwise it would differ.

#### Erik Horwath

Doc Al said:
You have the right idea. Start with the first equation, PV^(gamma)=constant. Then pick the variable you would like to eliminate. To eliminate P, substitute P = nRT/V (from the ideal gas law). Just plug it in and you'll see that it equals your second equation, TV^(gamma-1)=constant. (The constants will be different of course, but that doesn't matter.) Try it!

Then to find the equation you need to solve your problem, eliminate V in the same manner.
So that would mean P^(1-gamma)T^(gamma)=constant? Thanks for your help.

#### Doc Al

Mentor
Erik Horwath said:
So that would mean P^(1-gamma)T^(gamma)=constant?
Exactly right.

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