So now let's go around the cycle and just compare notes on what happens to the thermodynamic quantities as we do that.

现在让我们推导一下这个循环,比较一下这个过程中,热力学性质的变化。

麻省理工公开课 - 热力学与动力学课程节选

So we're going to go through a thermodynamic cycle, and here's what I want to calculate when we do this.

那么我们要推导,一个热力学循环,这是这个过程中我要计算的东西。

麻省理工公开课 - 热力学与动力学课程节选

And my purpose will be not to say something as a postulate, but to show you where everything comes from, and it's best for you if you try to follow the logic.

我的目的不是,简单地告诉你们一个假说,而是给你们讲清楚这个理论的来龙去脉,如果你们能理解推导过程那就再好不过

耶鲁公开课 - 基础物理课程节选

The first way is just to turn the crank on the math, and the second way is to do a little bit more imaginative about the process.

第一个方法就是纯数学推导,第二个方法我们将对,这个过程做一些物理图像的想象。

麻省理工公开课 - 热力学与动力学课程节选

And I wanted to do it a different way which is a little bit convoluted, but it introduces the idea of a thermodynamic cycle, and it's something that we're going to use a lot in the class.

现在我将用另一种,有些复杂的办法来推导这一关系，在这一过程中引入,我们今后会常接触到的,热力学循环的概念。

麻省理工公开课 - 热力学与动力学课程节选

Now if you look at my derivation here, there's one spot where I could have just stopped and proven my point without going through the whole thing.

如果仔细检查我的推导过程，你会发现其实,我们不用研究整个循环过程,就可以证明我们要证的公式。

麻省理工公开课 - 热力学与动力学课程节选

That is, this is derived in the case for reversible paths.

即这些都是通过利用可逆过程推导出来的。

麻省理工公开课 - 热力学与动力学课程节选

So this isn't the most useful form that we can have, but what we'll see shortly is that from this, we can then derive further criteria for essentially any set of variables or any set of external constraints, like constant temperature or pressure or volume and so forth that we might set.

所以这不是我们所能得到的最有用的形式，但是我们会很快看到，我们能够进一步推导出包含任意变量,或者任意约束的自发过程判断标准，比如说恒定的温度，压强,体积或者其他我们能够给出的约束。

麻省理工公开课 - 热力学与动力学课程节选