The kinetic theorey of gases

2010-05-27 7:17 am

In kinetic theorey of gases, there exists a term degrees of freedom. What actually this term means.
Also, in the proof of the theorey, it first considers a particle moving with velocity along the x-axis. Then the pressure is expressed in terms of the velocity with Newton's law. However, in the proof, it states that as the particle move randomly in all directions, the velocity of the particle:
v^2 = vx^2 + vy^2 + vz^2, where vx, vy and vz are velocities along x,y,z axis. And since the particle moves randomly,
vx^2 = vy^2 = vz^2, and v^2 = 3vx^2. Why this happens?

回答 (1)

天同

2010-05-29 8:16 am

✔ 最佳答案

Degree of freedom simply means the number of modes of motion which a gas molecule possesses.

Thus, a monatomic molecule has 3 degrees of freedom (i.e. translational motions in x, y and z direction), a diatomic molecule has 5 degrees of freedom (3 tanslational and 2 rotational), a polyatomic molecule has 6 degrees of freedom (3 tanslational and 3 rotational).
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It is already said that the molecule moves randomly. That means the molecule moves in the x, y or z direction with equal probability. Thus, you could not distinguish motions among the x, y or z directions.

Therefore, we would have vx = vy = vz
but because v^2 = (vx)^2 + (vy)^2 + (vz)^2
hence, v^2 = 3.(vx)^2

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