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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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Were going to make it for a mole of gas, T1 so it's R times T1, V and then we'll have dV over V.
假设是有一摩尔气体，那么就是R乘以，然后有dv除以。
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ArgV You can think of this variable Arg V as literally an array a sequence of chunks of memory that literally are back to back to back in memory, and when you say bracket zero, by convention, you are referring to the variables stored here.
你可以想象这个变量,按顺序排列的一块块内存,依次地在内存中紧邻着的，当你指明，按照惯例，涉及,存储的变量在这里。
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Therefore, mathematically at a given time t, we can trade t for v and put it into this formula.
因此,从数学角度来说,在给定的时刻 t,我们可以用 v 来表示 t,并代入这个式子
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In the case of France again, they are the work of a brilliant military engineer called Vauban, v-a-u-b-a-n.
例如法国,在佩皮尼昂 里尔 蒙梅迪等地方,这样的要塞城镇随处可见
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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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Now we're going to hear Beach Boys, IV I guess,with a three-chord chord progression and it's going to be sub-dominant , V dominant , I tonic .
而现在我们来听听貌似是沙滩男孩，三和弦进行，然后将会是次属音，属音，和主音。
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Suppose that in 2010, v.163.com I see a car in a junk lot.
假设2010年，更多公开课到,我在废品站,看到一辆车。
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So, in fact, as Thucydides tells us beautifully in Book V, when the two armies actually hit each other they have already made a slight turn to the right.
因此,事实上,像修西得底斯在第五册里优雅描述的那样,当两军真正开始接触时,他们已经略微向右转了
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Does anyone have a guess for v?
有人猜到，V，是什么了吗？
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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 we're going to start with a mole of gas, V at some pressure, some volume, T temperature and some mole so V, doing it per mole, and we're going to do two paths here.
假设有1摩尔气体，具有一点的压强p，体积，温度，我们将让它，经过两条不同的路径。
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D-A-V-I-D I'm not hardcoding in D-A-V-I-D anymore but I can still use a variable.
我不再把名字写死为,而是用一个变量来代替。
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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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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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D-A-V-I-D Well, if I've got a five-letter word like D-A-V-I-D, well, that's like five bytes and yet we only have the ability thus far in this class to return one thing at a time I can't return five bytes to you, but wait a minute, those bytes by nature of a computer are just stored in RAM.
好的，如果有5个字母的单词，如，那是5个字节,我们只能返回一个东西,而不能返回5个字节，等一下，这些字节被计算机本能地,存储在内存中。
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