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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？
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We saw that the Bohr model was able to correlate the observations of Angstrom, which had been formulated by Balmer.
知道了波尔模型,可以和阿姆斯特朗的观察相吻合，这观察后来被巴尔末推导出来相证实。
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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。
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Just go back as often as possible to this formula and work your way from there.
尽量多地复习这个公式,自己多推导几遍
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It seems like a logical extension of that formula to three assets and you can easily see how to extend it to four or more assets, it's just the logical extension of that.
这样就将前个公式推导为三个资产的情况,显而易见,你们可以将其运用到四个乃至更多资产的情况下，这只是对原始公式一个推导罢了。
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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
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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。
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And, I will go through the actual line by line derivation not because I want to do derivations in class.
我们要仔细讨论实际的线,和推导出来的线,并不是我想在这节课做推导。
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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。
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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。
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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。
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If you watch me do the thing on the blackboard, it looks very reasonable.
如果你只看我在黑板上的推导,觉得很有道理
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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
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Now let's get the energy for the line.
现在我们来推导线的能量。
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So I could have written right here immediately CvdT equals Cv dT, and that was the end of my derivation.
于是我在这里就可以直接写,来它等于，完成了整个推导。
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Cycles that are suggested that you go through and aren't gone through in class also sometimes turn up on exams too, by the way.
顺带一提，那些我建议,你们去推导，而没有在课上,推导的循环有时也会。
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That for an ideal gas it has to be the case that there's no volume dependence of the energy.
我们可以直接推导这个结果,即证明对理想气体，内能和气体体积无关。
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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。
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So let's just to see how you run through some of those calculations. Now let me just ask who here took 5.111? And who here took 5.112?
那么让我们看看怎样,推导这些反应，现在让我问一下,这里有谁学过5。111？谁学过5。112？
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I will only do them on one condition, and that is I want to be able to teach you what the assumptions are that underlie the points in the derivation.
只在一个情况下我才会做，那就是要能够教会你们,假设是,构成了推导的基础。
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And we can do that by going through and deriving What we'll call the fundamental equations of thermodynamics.
通过推导,所谓的,基本热力学方程可以做到这一点。
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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。
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This is the kind of thing you should be able to deduce.
你们必须掌握推导这类问题的方法
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But I'm never going to ask you to derive things.
但是我从来不会要求你们去推导这些。
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I'm going to find that, then I'll give you an example.
我会推导出来,之后再给你们举一个例子
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So let's just go through and do that.
我们现在开始详细的做这样一个推导。
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But the other reason to go through the thermodynamic cycles and really to develop great facility with them is because there are just an awful lot of things in nature and things that we build that run in cycles, where we want to calculate the thermodynamics, right.
但是要推导热力学,循环并为之发展一套,完善方法的另外一个原因是,自然界中或人造的那些,我们想计算它们的热力学的东西,有很多是以循环的方式运作的。
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You cannot pull that out of theory.
而不是从理论推导出。
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I'm not going to turn the crank here.
详细推导了。
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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。
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