Statistical mechanics, bernoulli's forumula - collision freqency

AI Thread Summary
The discussion centers on the concept of collision frequency in statistical mechanics, specifically referencing Kubo's formula. The formula indicates that collision frequency is derived from the ratio of momentum to the product of mass and distance. A clarification is made regarding the round-trip distance a molecule travels between collisions, emphasizing that it should account for the distance to only one wall. The participant realizes their mistake in counting the distance to both walls. The thread concludes with a question about whether to close the discussion.
AirTycoon
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Hello,
I am having trouble understanding collision frequency in following discussion from Kubo,
EtOMYXp.png


$$collision\ frequency = \frac{1}{\frac{l}{v_{x}}}=\frac{p_{x}}{ml}$$

What am I missing ?
 
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Between two collisions against the same wall, a molecule must travel a round-trip distance equal to twice the width of the container.
 
ah. I was counting the opposite wall too. Thank You.

ps. Should I close this thread now ?
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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