A diatomic ideal gas such as air..

AI Thread Summary
A diatomic ideal gas like air, with γ = 1.4, undergoes adiabatic expansion to 40 times its original volume, prompting questions about changes in temperature and pressure. Participants discuss the relevant equations, emphasizing the relationship between temperature and volume during adiabatic processes. The equation TV^(γ - 1) = constant is highlighted as crucial for solving the problem. Suggestions include deriving the necessary relationships from the ideal gas law and existing equations. Understanding these principles is essential for accurately determining the temperature and pressure changes during the expansion.
Physics321
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A diatomic ideal gas such as air, for which γ = 1.4, expands adiabatically to 40 times its original volume.
(a) By what factor does the temperature change?
(b) By what factor does the pressure change?

I'm not sure how to attempt/approach this one. If anyone has any suggestions, it would be greatly appreciated.

I tried using the equation T = T(not) - (mgh/R)*(gamma-1/gamma) but I didn't get anywhere, because I'm not sure where the expanding 40 times it's original volume comes in.
 
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For adiabatic expansion, there is a simple relationship that involves the initial temperature and initial volume, final temperature and final volume, and gamma.
 
Picture1.jpg


Are you talking about this equation? I see it relates pressure, volume, and gamma, but not temperature.
 
Physics321 said:
View attachment 23588

Are you talking about this equation? I see it relates pressure, volume, and gamma, but not temperature.

Yeah, there's another one like that, only it relates a product involving T and V before and after the expansion. You could probably derive it from the relation you posted above + the ideal gas law, or you could look it up. It shouldn't be too hard to find.
 
So I searched around and found this one. It relates 2 volumes and an initial temperature.

Picture2.jpg
 
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