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And it's always going to come down to calculating the appropriate free energy, and how it changes in the process.
这总是涉及到计算,适当的自由能，以及这些自由能在过程中如何变化。
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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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And so this, in fact, when you say your computer stores information as zeros and ones, A you've just typed the capital letter A, that's all that's going on inside.
事实上，当你说电脑以这些0与1进行信息存储时，你已经键入了大写字母，那就是在计算机内部发生的过程。
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The process to control it is intriguing and interesting but the heart of the computer is simply this notion that we build our descriptions, our recipes, on a sequence of primitive instructions.
这个控制它的过程很耐人寻味，很有意思,但是计算机的核心仅仅只是,我们在初始指令序列上，建造描述、方法的一个概念罢了。
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But the beauty in this calculation is it shows that this concept of electron sharing in an unequal manner is sound and it gets you into the right ballpark.
但在这个计算过程中,真正漂亮的是对电子,非平均共价的考虑很完全,从而指引我们向一个正确的方向思考。
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I don't find that my analysis is profound in the final answer, I just took some estimates using my data and, again, we could-- if someone wanted to argue with us they could argue with my estimates of the expected returns of the standard deviations and the covariances, but not with this theory.
我在计算过程中并没有做太深入的分析，我只是用我的数据做了一下大概的估计,我再说一次，我们可以-,如果有人想就这个问题与我们争辩,他们可以争论我对期望收益的估计,或是争论标准差和协方差的估计值，但并不会针对理论本身。
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In practice, most of the time we work with these two numbers, Ax and Ay.
在实际过程中,大多数时间我们就用 Ax 和 Ay 来计算
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All I'm doing here, nothing particularly exciting, I'm simply plugging this expression in for P and then I multiplied the whole thing out because it was all multiplied by q.
这些计算过程确实很枯燥,我只是把这个算式代入到P中,然后打开整理,因为每一项都乘以了q
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And we saw that in fact in this case delta S of mixing, we calculated it, saw that it is positive.
实际上如果我们计算气体混合过程中,熵的变化，我们会发现这个量是正的。
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This is a point that is often confusing, because you can think, well maybe I could calculate what the internal pressure is even for this very rapid process.
这一点可能让你们很困惑，因为你们可以想象这个过程，我也可以计算在这快速的变化中,内部压强是多大。
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Because it says, your program will still give you a value, but it may not be what you intended, and you can't always tell, and that may propagate it's way down through a whole bunch of other computations before it causes some catastrophic failure.
因为这意味着，你的程序依然会返回一个值，但是这个值可能不是你想要的，你可能还分辨不出来，而且这种情况会传播,结果会沿着正果计算过程传播下去,直到产生一个灾难性的错误。
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The body of that function looks exactly like the computation up above, except I'm simply using those in place of the specific message I had before.
方法体内部看起来,很像上面的计算过程,除了我用这些来替代了,原来的那些特殊信息。
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I'm going from V2 to V2 dv - what do you think this integral is? Right, W1 so this is easy part, zero here.
这样才保证了过程的可逆性,下面来计算，路径1的功。
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I am going to sum up the atomic orbitals that go into the molecular orbital, and they are going to have some coefficients.
我准备将原子轨道组合起来,进行分子轨道计算，这个过程还需添加一些系数。
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Let me write a function, in fact the literal thing I would do is to say, identify the things that change, give each of them a variable name because I want to refer to them, and then write a function that captures the rest of that computation just with those variable names inside.
让我来写个方法,实际上我的意思是，辨别出变化的东西,然后给它们逐个命名以区分,然后写一个用来计算,这些变量的,包括计算过程的方法。
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The purpose here is to look at a series of processes in which temperature is held constant, and we're going to calculate how much work we get from allowing a gas to expand under various conditions.
目的是让大家了解一下,几个保持温度不变的过程，然后我们将计算,气体在不同膨胀过程中,的对外做功。
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We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.
我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。
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It's the same computation. But this is a nice way of writing it, often called defensive programming.
这跟原来的计算过程没什么不同,但这是写代码的更优秀的一种方式。
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If I look at those two pieces of computation, I can see a pattern there.
我们可以看到这两块的计算过程，是有个模式的。
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As I said, what we want to do is, we want to count the number of basic steps it takes to compute a computation as a function of input size.
我刚才提到了，我们要建立，一个根据输入大小的方法来计算,一个计算过程需要的时间,建立这个方法需要几步呢？
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Alan Turing In 1936, that same guy, Alan Turing, showed that with six simple primitives, anything that could be described in a mechanical process, it's actually algorithmically, could be programmed just using those six primitives.
在1936年，还是那个人，展示了六个基本类型，可以在计算过程中,表达出任何含义来，其实这是演算性质的，可以根据六个数字编程。
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Computing square root. I'm going to capture it in a piece of code, I'm going to be able to refer to it by a name, and I'm going to suppress the details, meaning inside of that computation, you don't need to know what it does. You just need to know, if I give it the right kind of input, it'll give me back an input that satisfies the contract that I set up.
比如计算平方根,我会用一段代码来说明,我将给它命名,并且忽略细节,意思就是在这一段计算过程中,你不用知道它做了什么，你只需知道，如果我进行了正确的输入,它将会给我符合条件的输出。
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If you have an isobaric you're going to have to calculate where the energy changes, and that's a calculation that's likely on the homework and very like on an exam as well, too.
在等压过程中,我们需要计算能量的变化，我们在作业,和考试中,就会遇到这类问题。
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Our goal is to take problems and break them down into these computational steps, these sequence of instructions that'll allow us to capture that process.
我们的目标是得到问题,然后将问题分解为这些计算步骤，这些指令集,可以让我们看到这个过程。
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What that means, in a stored-program computer, is that I can provide to the computer a sequence of instructions describing the process I want it to execute.
它的意思就是说，我可以给一个存储程序计算机,提供一系列,描述我希望,能执行的过程的指令。
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So, let's calculate w1. The work for path one.
计算这两个过程中做的功。
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And I know energy is related to Cv through Cv dT etcetera.
我们可以计算,这两个过程中的能量差。
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Now what I want to do is put up a specific example of the cycle that can be undertaken inside here in an engine, and we can just calculate from what you've already seen of thermodynamics.
现在我想做的是,举一个例子,来具体说明热机内部的循环过程，同时我们可以利用热力学定律进行计算,看看热力学参量发生了什么变化。
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Second thing we've got to worry about is, what's a basic step? All right, if I bury a whole lot of computation inside of something, I can say, wow, this program, you know, runs in one step. Unfortunately, that one step calls the Oracle at Delphi and gets an answer back. Maybe not quite what you want.
我们需要担心的第二件事情就是，什么该作为一个基本的步骤呢？,如果我把一大堆的计算过程放到里面，我可以说，噢，这个程序你知道的，一步就完成了，不幸的是,这一步可能要靠预言家才能得到答案,这可能跟你想要的结果不太相同吧。
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Because in doing that, Python would then have a value that it could pass on into some other part of a computation, and if it wasn't what I wanted, I might be a long ways downstream in the computation before I actually hit some result that makes no sense.
因为如果这样做的话，Python会将,输入的值传递到下面的,一些运算中去，如果这个值的类型不是我想要的，我可能会在得到,一个毫无意义的结果之前,经历一个很长时间的,计算过程。
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