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And we saw that in fact in this case delta S of mixing, we calculated it, saw that it is positive.
实际上如果我们计算气体混合过程中,熵的变化，我们会发现这个量是正的。
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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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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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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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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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So, I just want to write a few examples down with a few values for delta u or delta H or delta S, and see whether we can get any clues from what we see.
我先写一些例子,例子包含一些内能，自由焓和熵的变化数值，然后看从中,我们能不能得到一些启示。
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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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Do we calculate, you know, delta S, delta u, delta H?
是否要计算熵的变化，内能的变化，自由焓的变化？
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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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Namely, it's delta S is greater than zero.
变化过程中熵的变化总是大于零的。
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Change in entropy is greater than zero for an isolated system.
对孤立系统,熵的变化是大于零的。
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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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And the useful outcome of all that is that p we get to see how entropy changes with one of those variables in terms of only V, T, and p, which come out of some equation of state.
这样做的重要结果是,我们得到了熵随着V，T或者,其中一个变量变化的情况，这些可以从状态方程得到。
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H We also saw that dS for constant H and p was greater than zero.
我们同样可以看到如果保持自由焓,和压强不变熵的变化dS也是大于零的。
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T That dS is greater than dq over T.
对吗，熵的变化dS大于热量dq除以温度。
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