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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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So what we've discovered from this relationship dq that du at constant volume is equal to dq v.
从这个关系式里我们发现,恒体积时的du等于恒体积时的。
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So the first path then, the first path, 1 constant volume constant V, so I'm going to, again, let's just worry about energy.
首先，是路径，等压过程。
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So I can make a quantity that I'll call V bar, which is the molar volume, the volume of one mole of a component in my system, and that becomes an intensive quantity.
所以我可以定义，一个叫做一横的量，这是摩尔体积系统中,一摩尔某种组分的体积，它就变成了。
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If you double the volume , the v doubles.
如果你把体积扩大一倍也会扩大一倍。
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v du/dV under constant temperature. du/dT v under constant volume. You use the Joule expansion to find these quantities.
像偏u偏v，恒温下的偏u偏,恒容下的偏u偏,你们知道怎么运用焦耳定律。
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And then V minus the excluded volume term is equal to RT. Two parameters, this is the attraction between two atoms or molecules in the gas phase.
以及V减去一个排斥项,等于RT，两个参数，这是气体状态下两个原子,或者分子之间的吸引力。
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b It's RT over molar volume minus b minus a over molar volume V squared.
它等于RT除以摩尔体积V杠减去,再减去a除以摩尔体积的V杠平方。
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V All right, or p is equal to a constant divided by volume.
或者p等于常数C除以。
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So we're going to start with a mole of gas, V at some pressure, some volume, T temperature and some mole so V, doing it per mole, and we're going to do two paths here.
假设有1摩尔气体，具有一点的压强p，体积，温度，我们将让它，经过两条不同的路径。
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V They do have the same temperature though.
不同，a，different，volume。,但是温度是一样的。
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a over the molar volume squared.
等于a除以摩尔体积V杠的平方。
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