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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。
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So, and of course, you know, keeping entropy as a fixed variable for a system like that is extremely cumbersome.
所以，对这样的系统要求它们的熵保持恒定,和一个非常笨拙做法。
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When we have an isolated system, the criterion that determineswhether something happens spontaneously is the entropy has to increase.
对于孤立系统,决定一个过程是否自发发生的判据为：,熵必须增加。
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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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And what's fallen out when we do that, because in each case, one of the first derivatives gives us the entropy.
当我们这样做时就得到了结果，因为在这些例子中，一阶导数是熵。
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The reason the entropy of the mixed gases is the highest is because that has the most possible configurations.
因为混合气体具有最多可能的状态,所以混合气体的熵最大。
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And the bigger lesson from that is that entropy, unlike energy u or enthalpy H, we could define an absolutely number for it.
热力学第三定律的一个更重要的推论是,与内能和自由焓不同，我们可以给上定义一个绝对的数值。
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But at the same time, entropy is going to be favoring whichever side has higher entropy, has more disorder, and there's a balance that's achieved.
但是同时熵的变化可能,支持反应向着具有更高熵更无序的方向进行，这就是最终达到的平衡。
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As soon as you allow anything to mix, like you might if you want to do any chemistry, entropy changes.
只要你允许物质混合，就像你做任何化学实验的时候要做的，熵就会发生变化。
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Still, the actual equilibrium depends on entropy also, not only on the energy.
而且，实际的平衡依赖于熵，而不仅仅是能量。
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And that's consistent with other things that we've seen, Remember the whole thing about the perfect crystal at zero degrees Kelvin has zero entropy It's completely ordered.
这和我们看到的其他东西自洽吗？,想想零摄氏度下的,完美晶体的熵为零,这是完全有序的。
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There's a balance here between ordinary energy or enthalpy and entropy.
通常所说的能量,或者自由焓和熵之间存在一个平衡。
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We looked at pressure change before, actually, in discussing the third law, the fact that the entropy goes to zero as the absolute temperature goes to zero for a pure,perfect crystal.
在讨论热力学第三定律的时候，我们讨论过压强变化,即对于纯净的完美晶体,随着温度下降到绝对零度熵也变成零。
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And just like we saw before for the case of entropy in an isolated system, now we have something we can calculate.
就像我们前面看到的,孤立系统的熵一样，现在我们有一些可以计算的东西。
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Even though the signs of the enthalpy changed, and the signs of the entropy changed because it's a combination of the two that matters.
即使自由焓的符号发生变化，熵的符号也会发生变化,因为这两部分都起作用。
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And this is the familiar result from ordinary mechanics, where you're not worrying about something like entropy for a whole collection of particles.
在普通力学中，如果不关注大量粒子的熵，诸如此类的物理量的话,这就是我们通常见到的结果。
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Well, I can, for any given case, measure the pressure, determine the entropy and I'll know what the slope of change will be.
好的，对特定的情况，我可以测量压强，确定熵,并且知道这就是变化的速率。
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OK, what we'll see shortly is that this will allow us to see that for an isolated system the entropy never decreases.
好，我们过一会,会看到,这将导致孤立系统的熵,永远不会减小。
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What happens to the thermodynamics parameters, and see the results in terms of the parameters including entropy.
以及用这些热力学参量,表示的物理量是怎么变化的，看结果是什么,这其中就包括了熵。
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Higher entropy basically because you're forming molecules of gas where there weren't any before, and there's more disorder in the gas phase than in the liquid. That is, the gas phase molecules have more freedom to roam.
高的熵是因为,我们产生了以前不存在的气体分子,气体的无序程度比液体大，换句话说,气相的分子，有更多的到处游荡的自由度。
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Be careful, and this is going to be especially complicated and confusing when we get to quantities that have a more obscure meaning like entropy.
大家要小心，如果需要测量的物理量,如熵，没有很明确的意义,那么着可能变得很复杂。
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Then the second derivative gives the change in entropy with respect to the variable that we're differentiating, with respect to which is either pressure or volume.
二阶导数给出熵,随着变量变化的情况，这些变量包括压强或者体积。
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Let's hang on for a little while longer to a set of conditions where we will maintain constant entropy, namely constant entropy and pressure.
我们先继续考虑,保持熵不变的情况，即保持熵和压强不变。
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So it seems like there's a favorable change in entropy going this way.
看起来在这个过程中熵增加是,有利于反应的。
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So that tells us what to do to know the entropy as the temperature changes.
这告诉我们当温度变化时,如何得到熵的数值。
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The volume is going to change, and we can see how the entropy changes.
体积发生变化，然后看熵如何发生变化。
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In other words, we choose a convention for the zero of entropy, so that then we can write entropies of products and reactants always referring to the same standard state.
换句话说，我们选择了一个,焓零点的约定，这样我们,就可以总是相对于同样的标准,状态写出生成物和反应物的焓。
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There is an absolute zero of entropy, and that's really what we learn.
而熵是有绝对零点的，这就是我们学到的。
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Can determine how entropy is going to behave as the volume changes.
这些偏导数,你就可以知道当体积变化时熵如何变化。
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That is, you've got lower energy on the right and also higher entropy.
这表明，你降低了能量,同时增加了熵。
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