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。

麻省理工公开课 - 热力学与动力学课程节选

so we're going to use this concept of the path to go from the initial point to the end point.

在处理状态函数时,路径的选取。

麻省理工公开课 - 热力学与动力学课程节选

But at some point you have to understand that the benefits of redistribution of wealth don't justify the initial violation of the property right.

但某种程度上说，你得明白,财富重新分配的好处,并不能为侵犯财产权正名。

耶鲁公开课 - 公正课程节选

By saying first element remember we start at as the initial indexing point.

我们说的第一个元素指的是,最初的开始索引点。

麻省理工公开课 - 计算机科学及编程导论课程节选

get back to the initial point is going to require some input from outside, like heat or extra work or extra heat or something because you've done an irreversible process.

如果要逆转它,回到初始点，就需要外界的投入，比如额外的功，额外的热量等等,因为你进行了一个不可逆过程。

麻省理工公开课 - 热力学与动力学课程节选

So there's going to be a line that's going to connect the initial point to the final point, and that line mathematically is not going to be the same as this one here.

连接绝热过程,初末态的曲线的方程，和等温线的方程,也不会相同。

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