RT2 So it's R T2, right, now we're at a lower temperature times log the log of V4 over V3.

等于，这时温度比刚才低,乘以。

麻省理工公开课 - 热力学与动力学课程节选

Cv+R=Cp Cv is equal, oh Cv plus R is equal to Cp it's a relationship that we had up here that we wanted to prove.

我们就得到了,我们一开始,想要证明的。

麻省理工公开课 - 热力学与动力学课程节选

So that's why we have this zero point here, and just to point out again and again and again, it's not a radial node, it's just a point where we're starting our graph, because we're multiplying it by r equals zero.

这就是为什么在这里有个零点，我需要再三强调，这不是径向零点，他只是我们画图的起始处，因为我们用ｒ等于０乘以它。

麻省理工公开课 - 化学原理课程节选

So we know it's moving on a circle of radius r.

因此这个质点始终在做半径为 r 的圆周运动

耶鲁公开课 - 基础物理课程节选

Were going to make it for a mole of gas, T1 so it's R times T1, V and then we'll have dV over V.

假设是有一摩尔气体，那么就是R乘以，然后有dv除以。

麻省理工公开课 - 热力学与动力学课程节选

So, let's say we start off at the distance being ten angstroms. We can plug that into this differential equation that we'll have and solve it and what we find out is that r actually goes to zero at a time that's equal to 10 to the negative 10 seconds.

也就大约是这么多,所以我们取初始值10埃,我们把它代入到,这个微分方程解它,可以发现，r在10的,负10次方秒内就衰减到零了。

麻省理工公开课 - 化学原理课程节选

We found that it's R log V2 over V1.

这是路径A，我们已经得到它。

麻省理工公开课 - 热力学与动力学课程节选

But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.

但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。

麻省理工公开课 - 化学原理课程节选