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If you have a quantity which is constant over any closed path, that quantity is a thermodynamics state function.
如果有一个物理量,对任何闭合回路积分是常数，这个物理量就是一个热力学态函数。
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That is, most processes that we're concerned with, they'll happen with something held constant like pressure or temperature or maybe volume.
这句话是说我们所关注的大部分过程，发生的时候都是保持某个量为常数,比如压强，温度或者体积。
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STUDENT: PROFESSOR: Yes, thank you. All right, it is constant. You keep sitting back there where I can't get to you. Thank you very much.
学生：【不解中】,教授：是的，是常数，如果，就是常数,你坐在那儿一动不动我没法找到你。
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But I know when I multiply a vector by a number, I get a vector in the same direction.
但是我所知道的是当矢量乘以一个常数,我会得到一个同方向的矢量
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So, first, if I point out when l equals 0, when we have an s orbital, what you see is that angular part of the wave function is equal to a constant.
首先，如果ｌ等于０,那就是ｓ轨道，你们可以看到,它波函数的角度部分是一个常数。
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If I have Avogadro number of these things in a long line, you can bet it is going to be a solid.
如果在一条直线上,这些东西有阿伏伽德罗常数那么多，你肯定会说它是固体。
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So for those people who took Intro Economics, which is most of you, this is a game, this a setting in which we have constant marginal costs.
大多数学过经济学导论的同学都知道,这里的边际成本是一个常数
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Wow, OK, maybe not so wow, but this is now constant. This is constant time access. So I can do searching in constant time which is great.
喔，当然，可能没那么,但是现在是常数级了,这是常数时间的访问。
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You'll also see that they have all the physical constants that you're going to need, and also a bunch of the actual equations that we've been using in the first couple weeks here.
大家还可以看到这里有,你可能会用到的所有物理常数，还有一堆公式,是那些我们这几周来一直在用的。
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We can make some substitutions here using some of the derivation on the previous board which will give us the Planck constant divided by 2 pi mass of the electron times the Bohr radius.
在这里我们也可以,用我以前在黑板上写过的一些词来取代它,得到的是普朗克常数除以2π电子质量,再乘以波尔半径。
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Obviously-- and that's a bad way of saying it, I said constant the previous time-- in the linear case, it's subtract by certain amount.
这么描述很不准确，我之前在，线性算法中也说了常数,它是每次减少固定的量。
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What is it when you run a chemical reaction under ordinary circumstances, what's constant?
如果你在通常的环境下进行化学实验,那么这些条件是什么？什么保持常数？
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It only cares what temperature is. If temperature is constant, there's no change in energy.
如果温度是常数,能量就没有变化，对理想气体。
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So the meaning of the constant is where was the object at the initial time.
常数的含义是,物体的初位移
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It's three different second derivatives in terms of the three different parameters.
它是用三个不同常数表示的,三个不同的二阶导数。
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It is true mathematically, you can add two numbers, but you've got to ask yourself,"What am I doing as a physicist when I add these two numbers?"
在数学上它是正确的,你可以引入这两个常数,但是你需要问问自己,当我引入这两个常数时,这么做有什么物理意义
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And the relationship that he put forth is that the momentum is equal to Planck's constant times nu divided by the speed of light, or it's often more useful for us to think about it in terms of wavelength.
爱因斯坦提出的关系式是,动量等于普朗克常数,乘以υ除以光速，或者用波长来表示,通常更容易让我们想明白。
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I have constant time access which is great, but I paid a price, which is I had to use up some space.
我的访问时间现在是常数级别，这个非常的棒，但是我也付出了代价，不得不使用更多的空间，在整数的例子中。
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By the way, I want to emphasize that I've named these constants to make it easier to change.
顺便说一下，我想要强调,我给这些常数命名是为了更方便之后更改。
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It's OK to use certain fundamental constants that come in a lot of calculators, so there's nothing we can do about that. That's OK.
当然允许使用,一些普通计算器里都有的基本常数，我们不会连这些都不让用，这是没问题的。
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and we like log algorithms, because they're really fast. A typical characteristic of a log algorithm is a pro-- or sorry, an algorithm where it reduces the size of the problem by a constant factor.
并且我们也很喜欢对数算法,因为它很快,对数算法的典型特性是高速，哦，抱歉，是他能以常数因子的速度,降低问题的大小，很明显。
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The heat-added, temperature, and this is a proportionality constant.
这是热，这是温度，这是比例常数。
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And what I am going to do is say start with this ion, add up the energy associated with the interactions between that ion and everybody else in the row and then multiply it by Avogadro's number, because that is the number of atoms there are in a row.
接下来我要从这一离子开始，加上相互作用的能量，也就是这一离子,和其它所有在这一行的离子之间的能量,再乘以阿伏加德罗常数，因为这是在一行的原子的数量。
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And what you can see is we have this new constant that we haven't seen before.
你们可以看到,这个新的常数,这是我们以前没看过的。
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For most problems on exams, those quantities are constant, independent of temperature.
然后对于考试中的大部分问题，这些量都是与温度无关的常数。
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And finally we have Planck's constant here, which we're all familiar with.
最后这个是我们，都很熟悉的普朗克常数。
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And that implies that since the quantity we want is given by this quantity, which is zero times a constant, the quantity we want is also zero.
因为我们需要的量,是由这个量乘以一个常数，因为这个量是零，因此我们需要的量也是零。
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And that factor is 4 pi times epsilon zero.
这个常数是4乘π再乘ε
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Typical characterization, not all the time, but typical characterization, is an algorithm that reduces the size of a problem by one, or by some constant amount each time, is typically an example of a linear algorithm.
我们学习过了线性算法，它的典型特征，不是通用的,但是比较典型的特征是，它是逐一减小问题的大小的，或者说是每次减小常数的大小。
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That's a new constant for us in this course.
这是我们这课里,新的一个常数。
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