Talk:Adiabatic invariant

rapid expansion

I disagree with the analysis of this edit ("Adiabatic Expansion of an Ideal Gas: Corrected the false statement that the temperature of the gas in an instantaneously expanded container does not change.") The editor did not correct a false example but rather analyzed a different case. If a fixed volume is expanded rapidly to a new fixed volume, then the final temperature of the gas will indeed be the same (ideally). There will be a transition state where the gas is moving and the local temperature is lower, but as soon as the gas bounces of the wall and remixes, the temperature will equal the original temperature. Quantitatively, the expansion of the box must occur fast compared to the acoustic transit time, but the temperature must be measured at a much later time. --Art Carlson (talk) 11:25, 10 January 2009 (UTC)

Magnetic Moment

From the section on The first adiabatic invariant, μ:

There are some important situations in which the magnetic moment is not invariant:

• Magnetic pumping: When μ is constant, the perpendicular particle energy is proportional to B, so the particles can be heated by increasing B, but this is a 'one shot' deal because the field cannot be increased indefinitely.

Can we clarify the above quote? Does it mean that in the first part, on magnetic pumping, the magnetic moment IS invariant? --User: Lenfreeman Lenfreeman (talk) 13:38, 24 January 2010 (UTC)

I don't understand your question. The article states that the magnetic moment is (usually) "a constant of the motion" = "invariant", and then lists three conditions for which this is not true. --Art Carlson (talk) 15:40, 24 January 2010 (UTC)

When μ is constant, the perpendicular particle energy is proportional to B, so the particles can be heated by increasing B

Sorry - but the section begins by indicating when the magnetic moment is not invariant (constant), but then says "When μ is constant, the perpendicular particle energy is proportional to B, so the particles can be heated by increasing B". I take this last sentence to mean that during heating the magnetic moment is still invariant? If not, in which situation would the magnetic moment be invariant?

Lenfreeman (talk) 16:16, 24 January 2010 (UTC)

I tried to make the section clearer. What do you think? --Art Carlson (talk) 18:10, 24 January 2010 (UTC)

Excellent - It's absolutely clear. Thanks.[[User:Lenfreeman (talk) 18:25, 24 January 2010 (UTC)]]

Entropy calculation from phase space volume for an ideal gas

I edited the section "adiabatic expansion of an ideal gas" to fix the derivation of the entropy from phase space volume.

- The gas in this derivation is implicitly assumed to be monatomic, and I made this explicit. If the gas isn't monatomic, I think you would calculate phase space volume from the surface area of a $2C_{v}N$-dimensional ball, instead.

- I included the formula for the volume of a 3N-1 dimensional sphere, since it includes an important factor of $\Gamma (3N/2)$.

- The gas states are redundant by a factor of N!, since the gas molecules are indistinguishable. Puffysphere (talk) 21:34, 8 March 2010 (UTC)

Unexplained notation

In the section Wien's Law the notation "< E_f >" is used but not explained.  --Lambiam 23:18, 27 June 2010 (UTC)