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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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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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I start off, either I take this path and carry on, or I take that path and carry on, but each box, if you like, gets touched exactly once.
程序开始后，或者采取这条路径然后继续，或者采取那条路径然后继续，但是每个图形，如果你喜欢这么说的话。
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Depending on what you call external and internal environment, this path that I'm tracing here, deep within your digestive system, is really directly connected to the outside world through both ends.
基于你们所谓的外环境和内环境,我在这里我所指的消化系统内部通路,它的两端确实与外界环境直接相通
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My path in life was fundamentally altered by just a handful of courses at this place and this was in fact one of them.
在哈佛所学的一些课程,从根本上改变了我的人生道路,这门课就是其中之一。
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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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Why? Because this path is an adiabatic path.
为什么？因为这条路径。
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OK. Note, by the way, if I chase through each possible path, like there's some IFs in here, if there's some places to go, at least in this piece of code, every possible path through this code ends in a return. And that's a good programming discipline, to make sure that happens.
注意一下,如果我跟进每一条可能的路径，像是这里的，起码在这段代码中就有很多走向，这段代码中的每一条可能路径,在结尾都会返回一个值,这就是一条很好的编程定律，请确保这样做。
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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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Cv Cv is going to be related to this path.
这个。
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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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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。
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And you already saw last time there was this relationship between the temperature and volume changes along an adiabatic path.
是条绝热路径，而上次你已经看到,沿着绝热路径温度和体积,的变化有这个关系。
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Now,this is a reversible adiabatic path, so there's a relationship that I'm sure you'll remember.
现在是可逆绝热过程，因此这里有一个关系式,我相信你们还记得。
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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
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The sum of path number 2 and path number 3 get me to the same place, so the energy change by going through this time path, this intermediate point here back all the way to final state should be the same the red path.
而经过路径2和3可以3,到达同样的末态，因此经过路径,2和3带来的能量的变化，与路径1带来的,能量变化相同。
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It configured the Mac or in this case, the Linux server to put it into my so-called path which just means I know where it is automatically.
在我的Mac机，或者是我们现在的这个Linux服务器上把它设置成,自动放到我知道的,路径下。
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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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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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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。
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And again, I want to stress this is a reversible path.
再强调一次，我们研究的是可逆过程。
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