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All right so I probably should have chosen a shorter number 71 because now I can't figure it in here, but let's call it 71.
好的，我可能应该选择一个更短的数字,因为我不能指出它，我把它叫做。
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Alex is going to get all the left wing votes, but there aren't enough left wing votes here, right?
亚历克斯将获得他左边左派的选票,但不是所有的左派选票,对吗
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How many people here are sort of complicated, ambidextrous, don't know, "Bit of the right, bit of left" people?
有多少人是有些不确定,左右都行,说不清,"时左时右"
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You always want to check your signs at the and because it's so easy to get the sign wrong, and I was hoping that it was right here because I wasn't sure, but it turned out to be right.
我们完成计算时，一定要记得检查符号,因为很容易弄错符号，刚才我就不太确定,是否弄错了符号，检查发现没有问题。
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My management doesn't ask me what I'm doing in here, all right? They don't know.
我的管理部门没有问我在课堂上做什么，他们根本不知道。
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I don't have time here to discuss this section right now, but you've already had some encounter with the incredibly impressive level of ingenuity and grotesquery in this remarkable passage.
现在我们没有时间来讨论这一部分了，但你们已经领略到了这一段中,给人深刻印象的,独创性和其中的怪诞。
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23456789 All right, here I gave it a big number, 123456789. And again, I don't want to bore you, but you can see what's going on here with this trend.
我给出一个大数字，又一次，我并不想令你们感到枯燥，但你们可以自己看看会发生些什么,这儿有个有趣的问题。
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The only other time we've seen a boom like this was right after World War II and that's shown by this line here; that wasn't as big.
我们可以看到,类似的繁荣,只在第二次世界大战之后出现过,就像这条线所显示的,这个增量不大
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Don't take those. Right here.
不要拿走那些，就在这。
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All right, so it looks like we weren't showing the percentages here, but it looks like hopefully most of you were able to get the correct answer of H2 being the limiting reactant.
看来我们好像没办法,显示结果的比例，但看起来大部分人,都能得到正确的结果,那就是H2是受限制的反应物2,看来现在我们还没搞明白。
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So again, for both heat and work we don't get the same result. Now let's look at our special function, right. So here's path A.
所以，再一次说明，对于热量和功,我们得到的结果是不同的,现在让我们看看我们的特殊函数。
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All right, it turned out that this thermometer here wasn't quite perfect either.
事实上,这样定义出来的温标。
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So we know that in each case the heat is going to be the opposite of the work, but the work isn't the same in these two different ways of getting from here to here, right. So let's just see it explicitly. Here's our qA.
所以我们知道在每种情形下功,与热量相差一个负号,但从这里到这里，在这两条路径,中的功是不同的，对吧？,那么让我们明确地看一下。
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Let's look at the show of hands? All right so this is the majority here. Good thing physics doesn't work on the rule of the majority otherwise we'd be in big trouble.
不可逆呢？请举手，好的,大多数人这么认为,真理并不掌握在多数人手里,否则我们就会有大麻烦了。
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And the logic is if you find somebody-- Crudely, if you find somebody with damage to this part of the brain right here and that person can't recognize faces for instance, there's some reason to believe that this part of the brain is related to face recognition.
这里的逻辑是这样的,比如说,如果你发现某人,大脑的右边这一部分受到了损伤,他无法进行面孔识别,那么就有理由相信,大脑的这部分是与面孔识别有关的
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There's a keyword, which I'm going to highlight right up here, print, which is in, I don't know what that color is, orange?
这里有个，我要高亮显示的，包含print的关键词，我不知道这是什么颜色，橙色么？
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This depends on the path. It tells you right here the path is constant pressure. These don't depend on the path, right. V doesn't care how you v get there. u doesn't care how you get there.
这由变化的具体路径决定,这个小脚标表明过程是恒压的,这些量都与具体路径无关,即不管是通过什么路径使得体积变化为Δ
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The game I just put up, that's a trivial example, it didn't really matter which equilibrium we played here, we just wanted to play an equilibrium, is that right?
但是现在讨论的这个小案例呢,到底达成哪个均衡并不重要,重要的是我们要达成均衡,是这样吧
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Right, you can't actually see the marginal revenue here.
实际上你们不知道边际收入是多少
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du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.
偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。
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