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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。
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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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You just need a few macroscopic variables that are very familiar to you, like the pressure, the temperature, the volume, the number of moles of each component, the mass of the system.
你只需要某些你非常熟悉的宏观变量,比如压强，温度，体积，每个组分的摩尔数，系统的质量。
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The volumes per mole of that stuff.
每摩尔物质的体积。
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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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And then we can take the derivative with respect to temperature, it's just R over molar volume minus b.
这样我们求,压强对温度的偏导数，结果等于R除以摩尔体积V杠减去b的差。
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In this case, V = /P. Have two quantities and the number of moles gives you another property. You don't need to know the volume. All you need to know is the pressure and temperature and the number of moles to get the volume.
以及气体的摩尔数,就可以得到第三个量,知道压强，温度和气体的,摩尔数就可以推导出气体的体积,这称为状态方程,它建立了状态函数之间的联系。
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Minus p, right? But in fact, if you go back to the van der Waal's equation of state b here's RT over v minus b.
再减去p，对吗，但是实际上，如果你代回范德瓦尔斯气体的状态方程,这里是RT除以摩尔体积减去。
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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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The property is the limit as p goes to zero of pressure times molar volume.
与摩尔体积的乘积,在气体压强p趋于0时的极限。
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So it's RT over molar volume minus b.
等于RT除以摩尔体积减去b的差。
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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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Equals a over molar volume squared.
等于a除以摩尔体积的平方。
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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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