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When in 1645 Milton finally publishes that first volume of poetry, the first poem that he places in this volume is the Nativity Ode, our poem today.
当1645年出版了首个诗集，他把《圣诞清晨歌》放在最前面，就是我们今天看到的这首诗。
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And this volume, temperature and pressure doesn't care how you got there. It is what it is.
另一个状态,也有一组确定的体积。
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So, I've got this tiny volume with, in the case of gold 79 plus of charge, and I've got some electrons out here somewhere, and the vast majority of the atom is nothing.
我认为这个小体积里面，比如金的79个正电荷，电子在外面的某些地方，原子里面大部分是空心的。
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So let me play this, so we may need to have high volume on this because this is pretty--this is--needs a little more volume .
接下来我要开始放了,音量可能要高一点,因为这很,这个视频的音量要高些
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So if we take this term, which is a volume term, and multiply it by probability over volume, what we're going to end up with is an actual probability of finding our electron at that distance, r, from the nucleus.
如果我们取这项，也就是体积项然后，乘以概率除以体积，我们能得到的就是真正在距离,原子核ｒ处找到电子的概率。
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So how would we go about solving this problem if I told you not only was there a maximum weight, but there was a maximum volume. Well, we want to go back and attack it exactly the way we attacked it the first time, which was write some mathematical formulas.
有些时候两个都重要,所以如果我告诉你这里不仅有,最大重量还有最大容量，我们应该怎么解决这个问题呢？,好了，我们想回过来然后,和第一次一样看看这个问题。
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If there were just-- if you were trying to create a positive reaction of antigens and it showed up naturally wouldn't it create this reaction anyway in terms of your body would create antibodies like the secondary response volume to antibodies?
如果这里仅有,如果在自然条件下,尝试建立抗原的阳性反应,抗体这是否会像这样反应,以你身体为例,你的身体是否会产生,同二次免疫一样的抗体浓度
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In this case here, our property is the value of the pressure times the volume, times the molar volume. That's the property.
或者电阻,对气体来说，它的特性是气体压强。
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And we combine this with first law, which for the case of pressure volume changes we write as this.
结合第一和第二定律,对于压强体积功我们可以这样写。
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And you already saw last time there was this relationship between the temperature and volume changes along an adiabatic path.
是条绝热路径，而上次你已经看到,沿着绝热路径温度和体积,的变化有这个关系。
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This is the fact that we occupy a finite volume in space, because they're little hard spheres in this molecule.
这是由气体分子在空间中,占据有限体积造成的,因为事实上它们是硬的小圆球。
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There's a volume, there's a temperature, than the pressure here. There's other volume, temperature and pressure here, corresponding to this system here.
温度等状态函数有本质区别，这个状态有一组，确定的体积，温度与压强。
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When I flail my arms around I generate work and heat. This is not a constant volume process.
这不是一个恒容过程,但如果我是一个系统，当我做这些的时候。
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This is an example where the external pressure here is kept fixed as the volume changes, but it doesn't have to be kept fixed.
在我们举的这个例子中,外界压强不变，气体体积改变。
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The way I've got this drawn, the volume is going up in the process. It's an expansion.
像我画的图这样，这个过程中,体积是增加的，这是个膨胀。
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In this case it relates the volume to the pressure and the temperature.
现在假想我们需要用,理想气体定律来设计一台机器。
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Yes, and if we have gases involved, it's pretty similar, but now what will have is something like this. We'll have a reaction vessel that's sealed, it's constant volume.
如果涉及了气体，情况也很相似，只是现在的装置是这样的,我们有一个密封的反应容器,它的体积是恒定的。
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So now, this equation here relates three state functions together: the pressure the volume, and the temperature. Now, if you remember, we said that if you had a substance, if you knew the number of moles and two properties, you knew everything about the gas.
压强，体积和温度,大家应该还记得,我们提过，只要知道气体的摩尔数,和任意两个状态函数,就可以推导出其他的状态函数，这样，我们可以把它改写成。
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In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
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So this is still adiabatic. It's insulated, but now it's constant volume, OK.
这仍然是绝热的，是隔热的，但现在它的体积是恒定的。
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Now, if this is an ideal gas, we know that pressure is equal to nRT over volume.
如果这是一个理想气体系统，我们知道压强等于nRT除以体积。
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OK, for constant volume, this is zero.
对于恒定体积过程，第二项等于零。
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And so this is one path, constant volume.
因此这是一条。
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And so this is a constant volume path then.
因此这是个等体过程。
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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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So I've got, this piston here is compressed, and I slowly, slowly increase the volume, drop the temperature.
这样，这个活塞就被压缩了，然后我再很慢很慢地增加它的体积，降低温度。
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So, you do this measurement, you measure with the gas, you measure the pressure and the molar volume.
现在让压强趋于，现在测量气体的压强，和摩尔体积。
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So what we've discovered from this relationship dq that du at constant volume is equal to dq v.
从这个关系式里我们发现,恒体积时的du等于恒体积时的。
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OK, now we actually would like to simplify this or to write this in terms of not the volume change, v2/v1 but the pressure change. So, we have V2 over V1.
接下来我们将要把问题简化,不用体积变化来描述，而改作用压强变化来描述，现在我们有。
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I mean, if the energy is lower to occupy a smaller volume, then if I have this room and a bunch of molecules of oxygen, and nitrogen and what have you in the air, and there are weak attractions between them, why don't they all just sort of glum together and find whatever volume they like.
我的意思是，如果占据小的体积会使能量降低，如果我有这样一个空间,和一些氧气，氮气和其他空气中有的气体，并且分子之间还有微弱的相互作用，为什么他们不黏在一起,然后占据他们所想要占据的体积。
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