A diatomic ideal gas such as air..

[Physics321]

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.

 

[cepheid]

For adiabatic expansion, there is a simple relationship that involves the initial temperature and initial volume, final temperature and final volume, and gamma.

 

[Physics321]

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

 

[cepheid]

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.

 

[Physics321]

So I searched around and found this one. It relates 2 volumes and an initial temperature.

 

[cepheid]

No, no, you're overcomplicating this. Look here:

http://en.wikipedia.org/wiki/Adiabatic_process#Ideal_gas_.28reversible_case.29

At the end of this section, you see:

TV^{\gamma -1} = \textrm{const.}

Which comes simply from the ideal gas law and the other relationship you posted in post #3.