分子運動論的一個問題

2010-12-01 2:53 am

先參考維基百科: http://zh.wikipedia.org/zh-hk/%E5%88%86%E5%AD%90%E9%81%8B%E5%8B%95%E8%AB%96

此分子每隔
圖片參考：http://upload.wikimedia.org/math/e/8/b/e8bbf08f31a9df44926739d70db8aee4.png
便撞擊該面一次，因此該面所受到的力量為：

圖片參考：http://upload.wikimedia.org/math/e/6/f/e6f0335563c4120525288f43b2d3d75c.png

為什麼這個time interval不是分子與牆壁撞擊的tme interval, 反而是分子沒有與牆壁撞擊的time interval?

其實我完全明白問題出在哪裡，但是想考考大家。

回答 (1)

天同

2010-12-05 9:13 am

✔ 最佳答案

Strictly speaking, the presentation of the equation described above is not completely correct.The force Fx is an average force arises becuase of molecular bombardment onto the container wall. In calculating the average, we need to find the total change of momentum within a given time interval. The average force, according to Newton's Second Law, equals to the total change of momentum in a unit time.

The change of momentum in one bombardment by a molecule = 2m(vx)
If for convenience, take a time interval of one second, the number of bombardment that takes place on a given wall N = (vx)/2L

Thus, the total change of momentum within 1 second
= N.(2m(vx)) = [(vx)/2L].(2m(vx)) = 2m(vx)^2/2L = m(vx)^2/L

It is clear that the factor (2L/(vx)) is by no means the impact time. In fact, it is an assumption in kinetic theory of gases that the impact time should be negligible. The term should be (vx)/2L, which indeed represents the number of collision of a molecule with the container wall in one second.

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