Description of Adiabatic Expansion

[I_laff]

I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result $TV^{\gamma - 1} = constant$ which I understand. I have also seen the a similar result, $pV^{\gamma} = constant$. But I can't see how to get from the first expression to the second. Any ideas?

 

[hilbert2]

If you put $\frac{PV}{nR}$ in place of $T$ in the first equation, doesn't it become the second one, assuming that the number of moles $n$ remains constant in the expansion?

 

[I_laff]

From doing that you get $pV^{\gamma} = R(constant)$. So you just define a new constant on the RHS that contains $R$?

 

[sophiecentaur]

Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?

 

[hilbert2]

Yes, it's a different constant then, the original one multiplied by $nR$.

 

[sophiecentaur]

If you don't have a textbook, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.

 

[I_laff]

Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?

You are probably right, however I don't have a textbook on thermodynamics. I thought of substituting $\frac{pV}{nR}$ but didn't see how to remove $nR$ from the final expression. Since they're constant, I guess it's obvious the new constant contains these terms.

 

[I_laff]

If you don't have a textbook, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.

Thanks, I'll check it out .

 

[sophiecentaur]

Thanks, I'll check it out .

There are other on-line sources which are an alternative to a textbook but Hyperphysics is fairly user friendly.