-
These two relations involving entropy are also useful because they'll let us see how entropy depends on volume and pressure.
这两个涉及熵的关系也非常有用,因为他们告诉我们,熵和体积，压强的关系。
-
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。
-
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。
-
So the probability of having an electron at the nucleus in terms of probability per volume is very, very high.
在单位体积内发现,一个电子的概率非常非常大。
-
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
-
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。
-
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。
-
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。
-
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。
-
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。
-
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。
-
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。
-
That is, most processes that we're concerned with, they'll happen with something held constant like pressure or temperature or maybe volume.
这句话是说我们所关注的大部分过程，发生的时候都是保持某个量为常数,比如压强，温度或者体积。
-
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。
-
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。
-
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？
-
The molar volume is being changed a little bit trying to make things collide with each other, they can't occupy the same volume.
摩尔体积发生了很小的改变,如果你试图使气体分子间相互碰撞，他们不能占据同一个位置。
-
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。
-
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。
-
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
-
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。
-
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。
-
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。
-
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。
-
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
-
Every time you do the experiment T in equilibrium with the heat bath at T, v2 you'll get the same p2 and V2.
与热库相接触的每次实验中,达到热平衡后的温度都是，压强都是p2，体积都是。
-
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。
-
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。
-
And the equation of state, pressure versus volume at constant temperature, is going to have some form, let's just draw it in there like that.
系统的态函数，恒温下压强比体积，变化曲线，就像这样。
应用推荐