Weighing a Gas

Can you weigh the gas in a closed container? The answer from Newton's laws is yes! If you weigh an "empty" compressed gas cylinder and fill it with high pressure gas, it will then weigh more on an ordinary scale since you are weighing the gas in the cylinder. This will be demonstrated with a single molecule moving vertically, but the same result is obtained with any number of molecules moving in random directions so long as the collisions between them are elastic collisions.

你能称量封闭容器中的气体吗？根据牛顿运动定律，答案是肯定的！如果你称量一个‘空’的压缩气瓶，然后向其中充入高压气体，气瓶的重量就会在普通天平上增加，因为你在称量气瓶中的气体。这个现象可以通过一个垂直运动的单个分子来演示，只要分子之间的碰撞是弹性碰撞，无论有多少个分子以随机方向运动，都会得到相同的结果。

The difference between the average force on the bottom and top of the container is just the weight, mg, of the molecule. This can be generalized to any number of molecules traveling in random directions.

容器底部和顶部所受平均力的差只是分子的重量 mg。这一结论可以推广到任何随机方向运动的分子。

If a molecule traveling in a random direction has a y-component of velocity, it will eventually collide with the top or bottom of the container. In an elastic collision with the fixed wall, the y-component of velocity will be reversed, giving a change in momentum of twice the mass times the original velocity. The force on the wall during that brief collision is quite high, but the much smaller average force of the collision is obtained by dividing the change in momentum by the entire round-trip time to the opposite end of the container and back. Taking an average force like this allows you to determine average forces and average pressures on the walls of a container of gas.

如果一个分子以随机方向运动，具有y方向的速率分量，它最终会与容器的顶部或底部发生碰撞。在与固定壁的弹性碰撞中，y方向的速率分量会被反转，导致动量的变化为两倍的质量乘以原始速率。碰撞过程中对壁的力相当大，但通过将动量变化除以容器到对面端点并返回的整个往返时间，可以得到较小的平均碰撞力。采用这样的平均力可以确定容器内气体壁上的平均力和平均压强。

The fact that the molecules may undergo many collisions on the way from top to bottom does not change this outcome. If a molecule has a certain momentum toward the bottom as it starts from the top, that net momentum toward the bottom will not be changed, even if it undergoes billions of collisions. It will transfer momentum to many other molecules and the particles which eventually reach the bottom with that momentum will exert the same average force as if the original molecule got there.

分子在从顶部到底部的途中可能经历许多碰撞，但这不会改变这一结果。如果一个分子从顶部开始具有向下的一定动量，即使它经历数十亿次碰撞，这个向下的净动量也不会改变。它会将动量传递给许多其他分子，最终到达底部的那些分子将对动量施加相同的平均力，就像原来的分子直接到达底部一样。

What do you think? If a closed truck is carrying a lot of birds, will the truck weigh less if the birds are flying around in the truck?

你觉得呢？如果一辆封闭的卡车载有很多鸟，当这些鸟在卡车内飞翔时，卡车的重量会减少吗？

Is the atmospheric pressure times the area of the Earth's surface equal to the weight of the atmosphere?