So I could get to that object either through this path or through that path, it didn't matter which path I use to modify it, I would see it when I looked at the other. Yes.

另外一条绑定获得这个对象,无论我通过哪个绑定来修改它，我都能在两个绑定中都看到做的改变，是这样的。

麻省理工公开课 - 计算机科学及编程导论课程节选

The reason for inexact doesn't mean it's a crummy measurement, t means that it's path dependent, and so the value of this integral depends on how you get from one to two.

这是因为它是,与积分路径有关的，因此这里的积分值，取决于从一端到二端的,具体路径。

麻省理工公开课 - 热力学与动力学课程节选

What about those who don't follow the path of righteousness, of justice, of Dike?

那些不走正直之路,正义之路,上帝之路的人又将如何呢

耶鲁公开课 - 古希腊历史简介课程节选

And as I followed many of the students after they graduate, whether the students who work with me here as undergrads or students who I tutored, when I followed the path,it wasn't just empty words.

据我了解，很多学生毕业后，无论是与我一起工作,还是我辅导的学生，当我了解他们的前路，并不是些空话。

哈佛公开课 - 幸福课课程节选

dU=CvdT So du is still going to be equal to Cv dT, and we're still going to be able to use the first law, all these things don't matter where the path is.

于是，第一定律也依旧成立，这些关系都与路径无关。

麻省理工公开课 - 热力学与动力学课程节选

So if I worry about energy I have a pretty good chance of extracting out these heat capacities, right, and I don't have to worry about exactly which path and I can really mix things up.

而能量与热容有密切的关系,从能量就可以就算出这两个热容，我不需要考虑到底是哪一条路径,可以随意计算。

麻省理工公开课 - 热力学与动力学课程节选

This depends on the path. It tells you right here the path is constant pressure. These don't depend on the path, right. V doesn't care how you v get there. u doesn't care how you get there.

这由变化的具体路径决定,这个小脚标表明过程是恒压的,这些量都与具体路径无关,即不管是通过什么路径使得体积变化为Δ

麻省理工公开课 - 热力学与动力学课程节选

So for an irreversible process, I wouldn't really be allowed to put a path there.

不可逆过程，是无法画出路径曲线来的。

麻省理工公开课 - 热力学与动力学课程节选

If it was non-reversible, I would be allowed to put an initial point and a final point, but I wouldn't be allowed to put a path between them like this, connecting them together.

如果是不可逆过程，我可以画出过程的初态点,和末态点，但是我不能再像这样,画出连接这两个点的，路径曲线来。

麻省理工公开课 - 热力学与动力学课程节选

All right, because energy doesn't care about the path.

与路径无关,只决定。

麻省理工公开课 - 热力学与动力学课程节选

Because I know energy doesn't care about the path.

由于能量不依赖于路径。

麻省理工公开课 - 热力学与动力学课程节选

I don't need to know about a specific path here.

这只涉及系统的状态函数。

麻省理工公开课 - 热力学与动力学课程节选

Now, I wanted to go to through this just to go through one cycle quickly because we're going to be doing these all the time, and the importance of the fact that the path doesn't matter, and you can always connect things together in a way, whatever you want.

我使用这种,利用热力学循环的推导方法的原因在于,今后我们，将经常使用类似的方法,大家要记住路径是无关紧要的，可以随意选取一条路径,来连接两个态。

麻省理工公开课 - 热力学与动力学课程节选

Path number 1 I'm going straight up in the V-T diagram.

路径1在T-V图上,竖直向上。

麻省理工公开课 - 热力学与动力学课程节选