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So now we have a relationship between the ratios of these volumes that are reached during these adiabatic paths.
现在我们有了一个联系,这些绝热过程中,体积比的关系式。
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In other words, if we don't have to worry about entropy or volume equilibrium is achieved when energy is at a minimum.
换句话说，如果我们不担心熵,和体积的平衡,那么能量就得是最小的。
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I'm going to say, quite to the contrary, the positive charge is concentrated at the center in a tiny, tiny, tiny volume.
我要说的是，完全相反，正电荷集中在中心,在一个非常非常小的体积内。
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But remember that we need to multiply it by the volume here, the volume of some sphere we've defined.
但记住我们需要把它乘以体积，乘以一个我们定义的壳层的体积。
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So, now you have a single molecule, very large molecule, with not just two binding sites but with ten binding sites.
所以如果你体内有一个细胞,一个体积很大的细胞,细胞表面不只有两个抗原结合位点,而有十个抗原结合位点
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Not to harp on the mathematical features of this, but cubing, AX*X*X you know, if you're starting to do AX star, X star, X, every time you want to cube some value in a program, it just feels like this is going to get a little messy looking, if nothing else.
不要总是说这个的数学特性，但是体积，你们懂的，如果你开始做，在一个程序中，每次你想算几个数值的体积，感觉它就变得,有一点凌乱的，如果没有其他的。
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STUDENT: You can't exceed the volume that the knapsack can hold.
学生：你不能超过背包,所能容纳物品的体积。
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So for the reversible process, the work done is the integral under the pressure volume state function, the function of state.
对可逆过程，做的功,是压强体积态函数曲线下，的积分面积。
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OK, now what we'd like to do is be able to calculate any of these quantities in terms of temperature, pressure, volume properties.
现在我们想要做的是能够利用,温度，压强和体积的性质,计算上面的物理量。
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A cubic kilometer of seawater, go into the ocean and imagine a box .
一千立方米的海水，想象一下一个体积为一千立方米的盒子。
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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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They make up about 45% to 50% of the volume of blood is red cells.
红细胞占血液体积的,45%到50%
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It's going to have some volume, temperature to begin with, and then we're going to do something to it.
气体有一定的，体积与温度，现在我们。
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And that property could be the volume, like if you have a mercury thermometer , the volume of the mercury.
这种性质可以是体积，如果你有水银温度计,水银的体积。
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We could just collect a bunch of data. For a material .What's the volume it occupies at some pressure and temperature?
对一种物质我们可以得到一系列测量数据,在给定的温度和气压下,它的体积是什么？
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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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Now, you know with constant volume, H now it's not going to be delta H that's U straightforward to measure, it's going to be dealt u, all right.
好，现在你们知道在体积恒定的条件下，我们得到的不是Δ,我们直接测量到的是Δ,好，但这基本上也是一样的。
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So if we actually go ahead and multiply it by the volume of our shell, then we end up just with probability, which is kind of a nicer term to be thinking about here.
乘以壳层的体积,我们就得到了概率，在这里从这个角度，理解问题更好一些,如果我们考虑的是。
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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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It's going to be the same temperature V+dV as before but the volume is V plus dV now.
将升温到跟路径1的结果一样,但是现在的体积是。
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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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And if you're below this temperature here, this quantity, p times v it would be negative.
压强与体积的乘积将变成负数，这可能吗？
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You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
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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 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, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
我现在所要做的一切就是,考察自由能对,温度，体积和压强的偏导数。
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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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I don't need to tell you the volume here, because you've got enough information to calculate the volume.
这里我不需要告诉你体积，因为你已经获得了足够多的信息,来计算体积。
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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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