We want to integrate. So let's take the integral of both sides, going from the initial point to the final point.
分别从初态,到末态做积分,消去微分。
I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了,因此可以用,理想气体状态方程消去。
The seconds cross out, the kilograms cross out, one of the meters crosses out from the top, so we're left with an answer in meters.
秒消掉了,千克消掉了,单位米和上面的一起约去了,所以我们得到的答案只剩下米。
So the trick is to eliminate time from this equation.
所以这里的技巧就是消去方程中的时间
So I took this to the other side and I divided through by 2b and the b here cancels.
通过移项和通分成2b,就可以消去b了
R So let's get rid of R in this expression here.
利用这个式子,我们就可以消去。
let's use the ideal gas law to get rid of the temperature.
我们用理想气体定律,来消去温度。
That's going to get rid of this minus 1 here.
这样就消去了幂次中的。
We divide that by the mass, so 0.12 kilograms, that's the mass of a regulation baseball for the major leagues, and the velocity of the baseball is 42 meters per second. So, we can cross out our units doing our unit analysis.
我们用质量来除它,质量为0,12千克,这是大多数联赛规定的棒球质量,棒球的速度为42米每秒,所以,我们可以消去单位,来做单位分析。
So let's see how we can eliminate time.
我们来看看如何消去它
Somehow I've gotta get rid of the temperature and make it pressure instead.
应当用压强,来消去温度。
so you can eliminate.
这样就可以消去其中一个
So, when you divide by m, m cancels and everything falls at the same rate on the surface of the Earth.
因此,当等号两边除以 m 时,m 被消去了,在地球表面的所有物体,都以相同的加速度下落
We want to do that because we have too many variables here. We've already got dV p we'll get rid of p as an additional variable and replace it with V which is already in here.
我们之所以要那么做,是因为这儿有太多变量了,我们已经有了dV,我们要把,作为额外的变量消去,用已存在的V代换它。
By the way, that's a very remarkable property of the gravitational force-- the cancellation of the two ms.
顺便说一下,这是重力的一个重要属性,即可以消去等式两边的 m
We'll substitute that in, and the T dS terms are going to cancel.
将其代入,消去TdS项。
Once you've got that, one derivative will give you the velocity, then in a crunch you can eliminate t and put it into this formula.
一旦你得到了这个,求一阶导数就能得到速度,然后你可以消去t,把它代入这个式子
This time, the T dS terms are going to cancel.
这次TdS会被消去。
the Ax prime will drop off.
x 就被消去了
pxa So what happens when we add a 2 p a and we subtract from it a 2 p x b, or the same with a 2 p y a subtracting a 2 p y b, is that we're actually going to cancel out the wave function in the center, so we now have 2 nodal planes.
当我们用,减去2pxb时,或者是2pya减去2pyb时,我们会消去,中间的波函数,所以现在我们有两个节面。
Banish t everywhere.
将 t 全部消去
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