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And the path that I'm describing then, let's assume that we're raising the temperature up is this path right here.
经过一个，等压过程,路径就是这样。
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That’s my career path, but you're in New York,
那就是我的职业规划，但是在纽约，
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Path number 2 on my diagram it's a reversible, this path number 2, it's a reversible constant pressure path.
路径，首先是一个，等压过程。
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There's a continuous path from the outside world right through the intestine.
从体外经由肠道的路径,是一条连贯的通道
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But it's really a chance, especially for those less comfortable, to be set off on a very specific path.
这的确是一个机会，特别对于那些不怎么舒适的，这是通过,特殊途径开始的好机会。
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End up where you started. It's not quite the same as the shortest path, and figure out the way to do that that involves spending the least money. Or the least time, or something else.
最后回到最初的地方,这和最短路径问题有些不同,需要找出一条花费最少,或者费时最少或者满足其它条件的路径。
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A "way" is a path, but how can there be a path if it's not trodden?
路“指的是道路，但既然是道路怎么会没有人走过呢？
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And our job is to find out what is the mathematical description of this path, this line in p-V's case that connects these two point.
我们的任务,就是找出，描述这条曲线的方程。
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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。
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A OK, so that's path A.
好，这是路径。
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So again, for both heat and work we don't get the same result. Now let's look at our special function, right. So here's path A.
所以，再一次说明，对于热量和功,我们得到的结果是不同的,现在让我们看看我们的特殊函数。
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So if I take p times V to the gamma, anywhere on the path, it's going to be equal to the same relation This is going to be true for any point on the path.
结果都，将等于，初态点的,只要在这条路径上。
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All right, let's complete the cycle now, 3 the path number 3 here.
最后，来看路径。
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You just change volume to pressure and basically you're looking at enthalpy under a constant -- anything that's done at a constant volume path with energy, there's the same thing happening under constant pressure path for enthalpy.
可以看到这就是把体积换成了压强,一般我们都是在一种恒定状态下,考虑焓的，任何在恒容条件下,能伴随能量变化的东西，也在恒压条件下伴随焓同样地变化,所以你可以经常。
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And tomorrow it's recitation, we'll spend quite a bit of time on shortest path problems.
也就是说我们会在最短路径问题上,花上很多时间。
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So there's a return branch on every possible path through the code. And that's valuable, it's something you want to think about as your right your own.
所以代码中每条可能的路径,都会有一个返回值分支，这是非常有价值的,当你自己写程序的时候也应该考虑这件事。
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So that's our work in this path and heat.
这就是这个过程中的功和热。
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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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So path number 1 went from i, f let's call this path up here. went to f, and this is how much energy change there was.
从i出发，经过路径1到达，能量的变化是这么多。
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