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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 this unique temperature and unique pressure defines a triple point everywhere, and that's a great reference point.
这样，无论在何处,三相点都具有相同的温度和压强,十分适合来作参考点。
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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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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。
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On the other hand, temperature, volume and pressure are variables that are much easier in the lab to keep constant.
另一方面，温度，体积和压强,在实验室中比较容易保持恒定。
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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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Because it's so important. And I should add and also under reversible work, where the external pressure is equal to the internal pressure.
而且我还要说应该在外部压强,和内部压强相等的,可逆过程中引入它。
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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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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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p2 One of them is going to end up at pressure p2 p3 and the other is going to end up at pressure p3.
其中一种末态压强为2,另一种末态压强为。
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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。
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are all functions of state and parameters that we can control like temperature and pressure.
公式里面的全部都是态函数,我们控制态函数的参数比如温度或者压强。
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Your plant is going to blow up, because the ideal gas law works only in very small range of pressures and temperatures for most gases.
理想气体定律,只在一个很小的压强,与温度的范围内适用。
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Whereas under these conditions, these quantities, if you look at free energy change, for example at constant temperature and pressure, H you can still calculate H.
但是，在这些条件下，这些物理量，如果我们考察自由能的变化,例如在恒定的温度和压强下，我们仍然可以计算。
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For instance, the pressure and the temperature, or the volume and the pressure.
比如压强和温度，或体积和压强。
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It's a state function, so we're at constant temperature and pressure, and now we want to consider some chemical change or a phase transition or you name it.
这就是态函数，我们处于恒定的温度和压强之下，然后考虑某些化学变化或者相变,或者你想考虑的东西。
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This is a point that is often confusing, because you can think, well maybe I could calculate what the internal pressure is even for this very rapid process.
这一点可能让你们很困惑，因为你们可以想象这个过程，我也可以计算在这快速的变化中,内部压强是多大。
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We start at p1, V1. and p external is equal to zero.
从状态开始，外部压强为零。
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We know the pressure is equal to force per area.
我们知道压强等于力除以面积。
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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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But now, what happens if, instead we look at what happens when we go to some state one to some other state two and it's the pressure. Or the volume, that changes.
但是现在，我们看看如果,我们关系从状态一变化到状态二时,体积或者压强发生变化。
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You've got to put more pressure on one side than the other if you want to push that gas through the throttle, right? So this is where the time scale issue comes into play.
如果你想让更多的气体通过节流阀,应该使一边的压强,大于另一边，是吗？所以这就是,时间尺度发挥作用的地方。
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If I place my container of gas on the table here, and I come back an hour later, the pressure needs to be the same when I come back Otherwise it's not equilibrium.
如果我把装气体的容器放在桌子上，一小时以后我再回来时,气体的压强应该是不变的,否则它就不是平衡的。
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If I stop, if I move slowly, if I move more slowly then these two will want equilibrium.
如果我停下来，如果我缓慢地移动活塞,非常缓慢，结果这两个压强会平衡。
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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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Because what we've done is we forced p, pressure here, to be equal to the external pressure.
因为这里我们让内部的压强，等于外部的压强。
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All right, let's take the example of, the extreme example, let's go to the extreme example where p external is really small.
好了，现在我们来，看一个，极限情况,当外界压强非常小。
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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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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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