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We're not going to have the constant pressure heat capacity, we're going to have the constant volume heat capacity, right.
这里出现的,不是等压热容,而是等体热容。
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So, we do an integral over a path, dT for the heat capacity along that path, dT.
因此，我们沿着路径做一个积分，热容。
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It works its magic, again, through purely instrumental means, so we can't really call those songs, and this puzzled me.
纯器乐的演奏方式,容我重申,能产生神奇的效果,所以我们其实不能把器乐称为歌曲,这让我很困惑
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Then he said, "Let me go, for dawn is breaking." But he answered, "I will not let you go, unless you bless me." Said the other, "What is your name?"
那人说，“天黎明了，容我去吧，“但他说，“你不给我,祝福，我就不容你去，“那人说，“你名叫甚么？“他回“
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And Manifest Destiny was the engine of capitalism, make no mistake.
而且,命运天定思想,是资本主义的发动机,这点无容置疑
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Let me talk a little bit about that context.
容我略谈一下当时的脉络。
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He had not only written really quite daringly on behalf of the execution of this particular king, but he wrote another pamphlet, Eikonoklastes , which is a shocking defense of just regicide in general - not just in England, but as a kind of political principle.
他不仅对处死国王一事大胆的发表言论,还写了另外一本书，《圣容破坏者》,这本书为正义的弑君做了惊人的辩护,-不仅是在英国的这次弑君，还是一条普遍的政治原则。
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I didn't even need to know that heat capacity of the product, right. Because it's effect the thermal mass of the product is negligible compared to the thermal mass of the calorimeter.
我甚至不需要知道生成物的,热容是多少，因为生成物的,热质量的作用相比于,量热计的热质量是可以忽略的。
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You're allowed Cv comes out here for this adiabatic expansion, which is not a constant volume only because this is always true for an ideal gas.
绝热过程写下,这个式子是因为它对理想气体都成立，并没有用到等容过程的条件,只用了理想气体的条件。
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You just change volume to pressure and basically you're looking at enthalpy under a constant -- anything that's done at a constant volume path with energy, there's the same thing happening under constant pressure path for enthalpy.
可以看到这就是把体积换成了压强,一般我们都是在一种恒定状态下,考虑焓的，任何在恒容条件下,能伴随能量变化的东西，也在恒压条件下伴随焓同样地变化,所以你可以经常。
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for instance, for the thermos with the coffee in if you place the boundary in the inside wall of the glass or the outside wall of the glass and the inside of the thermos, that makes a difference; different heat capacity, etcetera.
比如说，对于装咖啡的热水瓶来说,你把边界设置在瓶胆的内壁上,或者设置在瓶胆外壁上,或设在热水瓶里面，情况都是不一样的;,有不同的热容等等。
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Heat capacity relates the amount of heat that you add to the system to the change in temperature, and this is the relationship.
热容联系起给系统提供的,热量和温度的变化，关系式是这样的：
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Ordinary heat capacities are in Joule's per Kelvin mole, not kilojoules, right.
一般热容的单位是焦耳每摩,而不是千焦。
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Heat capacity depends on path.
热容是与路径有关的。
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Now, I know how to relate the heat flow to temperature change, through the heat capacity.
现在我知道怎样把能量的流动,和温度的变化联系起来，通过热容。
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So if I worry about energy I have a pretty good chance of extracting out these heat capacities, right, and I don't have to worry about exactly which path and I can really mix things up.
而能量与热容有密切的关系,从能量就可以就算出这两个热容，我不需要考虑到底是哪一条路径,可以随意计算。
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It's not constant pressure, because we have a delta p going on. It's not constant volume either.
也不是恒容，这个限制,是这个实验的限制。
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This one turns out to be the heat capacity, and this one turns out to be something that we measure in the Joule-free expansion.
其实，这就是热容，这是焦耳自由膨胀实验中,我们要测量的物理量。
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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Today we're going to talk about heat capacity.
今天我们将要讨论热容的概念。
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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 just how much heat is involved when we change the temperature. Now, the products have some heat capacity associated with them right, it takes a certain amount of heat if we make their temperature change, to either put it in or take it away, depending on which direction the temperature is changing.
问题就是当我们改变温度时,有多少热量发生了转移,生成物具有一定的热容,如果我们改变,它们的温度，就要输入或,提取一定的热量,这取决于温度改变的方向。
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So we immediately get du at constant S and V is less than zero.
这样我们马上就得到以下结论：,在等熵，等容条件下dU必须小于零。
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And that generally is just given by the heat capacity the calorimeter times delta T, right.. Because the heat capacity of the calorimeter just like this thing is not strongly temperature dependent, OK.
一般它就由量热计的热容,乘以ΔT给出，因为，量热计的热容,就像这张桌子一样,并不强烈依赖于温度。
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