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"His name is John Barovetto, B-a-r-o-v-e-t-t-o.
VOA: standard.2010.05.31
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A It tells me that the partial of A with respect to T at constant V is minus S. Right?
他告诉我们,在恒定体积下对温度的微分等于负S，对吗？
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French universities are named very poetically, Paris I,II,III,IV,V,VI, all the way through XIV, which is a real hole, or XIII is probably the worst.
巴黎的大学命名得都很有诗意,巴黎第一大学,第二大学,第三大学,以此类推,一直到第十四大学,这是真实存在的,第十三大学可能是最差的
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So I can make a quantity that I'll call V bar, which is the molar volume, the volume of one mole of a component in my system, and that becomes an intensive quantity.
所以我可以定义，一个叫做一横的量，这是摩尔体积系统中,一摩尔某种组分的体积，它就变成了。
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This is his picture of Charles V at a battle in Germany in 1648.
这是一张查理五世,在1648年德国战争中的画
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So here's a program called Arg V, this is fancy speak for argument Vector, a list of arguments for the left or right.
这里有一个叫做ArgV的程序，这个设想讲述了,参数矢量，从左到右的一列参数。
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You know that if you took a derivative of this, you will find v of t is v0+at.
如果你对这个式子求一次导,你将会得到v=v0+at
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pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
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So if delta v is negative, in this case delta v is negative, OK, delta v is negative, pressure is a positive number, negative times negative is positive, work is greater than zero.
也就是当活塞,压缩气体的时候，做的功是正的，按照这一规定,我们需要在这里，加上一个负号，这是习惯规定。
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And so now we have this quantity, p times v bar, and the limit of p goes to zero is equal to a constant times the temperature.
不仅仅对氢气或氮气适用，在p趋于0的极限下,它适用于任何气体。
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D-A-V-I-D So when you get a string like D-A-V-I-D, what's really happening is inside your computer's RAM is going a byte where there's some zeros and ones.
譬如你有这么一个字符串，而在你电脑的RAM里将会变成,一个个由0和1组成的字节。
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But before you even do that, I want to define for you an important concept, which is the velocity at a given time, v .
但在这之前,我要给你们定义一个重要的概念,也就是给定时刻的瞬时速度v
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Well, turns out that with arrays, not to make this too trippy too soon, but Arg V bracket something is a string, you can also use square bracket notation to go to a specific letter in a string, because little teaser a string is just an array.
好的，结果用那个数组，不要使这个很快引起幻觉，但是Argv什么的，是一个字符串，你也可以用方括号定位到,字符串中的一个特定的字母，因为一个字符串只是一个数组。
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I'm pressing on the gas. So I expect that to be a positive number. The pressure is constant 0 p. The V goes from V1 to zero.
我们对气体加压,所以这应该是一个正数,压强是常数，p，V从V1变成。
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In other words, u is a function of T and V.
话句话说，u是T和V的函数。
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And the point is that the second derivative of A, with respect to V and T in this order is the same as the second derivative of a with respect to T and V in this order.
问题的关键在于A的二阶导数，对V和T以这样一个顺序求导,和对T和V以这样一个顺序,求导是一样的。
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The typical vector is called V or A or B something with an arrow on it.
表示矢量时一般在,字母 V,A 或者 B,上面加个箭头
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take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.
对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r
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The time, in fact, is v-v0 over a.
实际上,运动时间为/a
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v We don't know what it is yet. In order to change this from a p to a V, you have to use the chain rule. So let's use the chain rule.
为了把这里的p变成,我们需要利用链式法则,好，让我们使用链式法则。
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V All right, or p is equal to a constant divided by volume.
或者p等于常数C除以。
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So I just have to see, oh, here's a D, let me keep looking, D here's an A, keep looking here's a V, here's an I, here's a D and yet, and this is one tidbit we introduced a week or so ago, how do I now know if I'm just given the address of the start of the string where the end is?
我只需要看到，哦，这里是一个D，让我接着往下看，这里是A，接着这是V，这是I，这是,然而，这是我们一周以前介绍的花絮，如果你给我一个字符串开始的地址,我怎么知道它什么时候结束？
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Well, Arg V bracket 1, is, in fact, a string.
好的，Argv，实际上是一个字符串。
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As long as we understand that, we can do this cancellation and this says on the left-hand side the change in the quantity v square over 2 is a times the change in the quantity x.
只要我们明白这一点,我们就可以这样做简化,在等号左边,v^/2的变化量,为a乘以x的变化量
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Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.
我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分
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