All right, so I need to tell you the path, when I go from one state to the other.
好,当我从一个状态过渡到另一个状态时,我需要告诉你们路径。
So, the first obvious one is to take V1 to V2 first with p constant. So take this path here.
从初态到末态可以有无数种路径2,甚至像这样,我们只研究两种。
And it tries to find the shortest way, subject to those constraints, to get from Point A to Point B. And there are many, many other instances of this kind of thing.
然后谷歌地图开始寻找,满足这些条件的从A地到B地最短路径,还有很多这样的例子,明天我们会再复习一遍这些内容。
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。
It's going to be the same temperature V+dV as before but the volume is V plus dV now.
将升温到跟路径1的结果一样,但是现在的体积是。
For instance, you want to know how much energy you're going toget out from doing this expansion.
比如,你想知道在这个膨胀过程中,到另一个平衡态的路径。
So we know that in each case the heat is going to be the opposite of the work, but the work isn't the same in these two different ways of getting from here to here, right. So let's just see it explicitly. Here's our qA.
所以我们知道在每种情形下功,与热量相差一个负号,但从这里到这里,在这两条路径,中的功是不同的,对吧?,那么让我们明确地看一下。
I take V1 to V2 first, keeping the pressure constant at p1, then I take p1 to p2 keeping the volume constant V2 at V2. Let's call this path 1.
容易计算的路径,第一条路径,是首先保持压强不变,体积从V1压缩到。
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