"The point is, that what we are looking for is not just to continue on the same path, we want to leap into the future.

VOA: special.2010.04.28

So if you need the help of the notes it's in there but I would urge you to work through it on your own, and it's the following: let's start with the same path A, all right?

如果你需要帮助，可以去看讲义,但我还是希望你们自己去推导它,它是这样的，让我们从：,相同的路径A开始，好吗？

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 计算机科学及编程导论课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选