So it's a really powerful and simple formalism, once we set up what is needed the go through it, right?

因此这是一种很强大而简单的形式,一旦我们定下需要什么,就可以推导出它，对吧？

麻省理工公开课 - 热力学与动力学课程节选

OK, this is only true for an ideal gas, and we went through that mathematically where the, with a chain rule.

这一关系只对理想气体成立，上节课我们,用链式法则推导出了这一关系。

麻省理工公开课 - 热力学与动力学课程节选

I have shown that by taking Avogadro's number of individual ion pairs and putting them all together in a line, the system's energy became more negative.

我推导出了,从每一个离子对中抽出阿伏加德罗常数,再把它们放在一起在一列中，这个系统的能量就变得更负。

麻省理工公开课 - 固态化学导论课程节选

If it's something else, you will have to deduce another law.

在其它情况下,你会推导出其它的定律

耶鲁公开课 - 基础物理课程节选

On the one hand, even if it were true that the soul must be non-physical in order to grasp the non-physical forms, wouldn't follow that the soul will survive the death of the body.

一方面,即使,灵魂必须是非现实的,以便来认知非现实的型相,也没法推导出,灵魂可以在肉体死亡之后存活

耶鲁公开课 - 死亡课程节选

What Hicks said is that in these term structures, actually, I've just showed the one-period, he had one-period forward rate-- but you could do it over any combination and you can get forward rates of any maturity at any future date.

希克斯指出利率期限结构中,我刚才给你们演示了,希克斯是如何推导一年期远期利率的,但是你们通过其他组合重新推导,还算出未来任意时刻,期限的远期利率

耶鲁公开课 - 金融市场课程节选

So I just want to use that again and again, starting from that, for various different sorts of conditions andderive the criterion for equilibrium in each set of conditions.

所以我将会一遍又一遍地使用这个公式，从这个公式出发，在各种条件了,推导出,任意条件下的平衡条件。

麻省理工公开课 - 热力学与动力学课程节选

You cannot pull that out of theory.

而不是从理论推导出。

麻省理工公开课 - 固态化学导论课程节选

Now there's a second formula one derives from this.

现在可以从这个式子推导出第二个式子

耶鲁公开课 - 基础物理课程节选

In this case, V = /P. Have two quantities and the number of moles gives you another property. You don't need to know the volume. All you need to know is the pressure and temperature and the number of moles to get the volume.

以及气体的摩尔数,就可以得到第三个量,知道压强，温度和气体的,摩尔数就可以推导出气体的体积,这称为状态方程,它建立了状态函数之间的联系。

麻省理工公开课 - 热力学与动力学课程节选

So now, this equation here relates three state functions together: the pressure the volume, and the temperature. Now, if you remember, we said that if you had a substance, if you knew the number of moles and two properties, you knew everything about the gas.

压强，体积和温度,大家应该还记得,我们提过，只要知道气体的摩尔数,和任意两个状态函数,就可以推导出其他的状态函数，这样，我们可以把它改写成。

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

And the purpose of this course is to show you over and over and over again that starting with those one or two laws, you can deduce everything, and I would encourage you to think the same way.

这门课的目的,就是要反复告诉你们,从其中的一两条定律出发,你可以推导出一切,我鼓励你们用同样的方法来思考

耶鲁公开课 - 基础物理课程节选

You can now collect the whole expression as something something i plus something something j.

你们现在可以推导出完整的表达式,用 i 和 j 相关的式子来表示

耶鲁公开课 - 基础物理课程节选