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Let's try it with a different equation of state, that isn't quite as simple as the ideal gas case.
考虑一个不同的状态方程，这状态方程不像理想气体状态方程那么简单。
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So let's take our one model that we keep going back to Equation of state, and just see how it works.
我们回到经常使用的理想气体模型,或者说状态方程。
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I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了，因此可以用,理想气体状态方程消去。
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For real gases, there's a whole bunch of equation the states that you can find in textbooks, and I'm just going to go through a few of them.
这是理想气体的状态方程,对实际气体,你可以在教科书里，找到许多描述它们的,状态方程。
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Or, if we know the equation of state from a model, ideal gas, van der Waal's gas, whatever, u now we can determine u.
或者如果我们知道模型的状态方程,比如理想气体，范德瓦尔斯气体，无论什么，我们就可以利用状态方程得到内能。
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And you can find these compressibility factors in tables. If you want to know the compressibility factors for water, for steam, at a certain pressure and temperature, you go to a table and you find it.
各种气体的压缩系数,想知道水或者水蒸气,在某个温度和压强下的，压缩系数，查表就行了，这是实际气体状态方程的。
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So from measured equation of state data, or from a model like the ideal gas or the van der Waal's gas or another equation of state you know this.
所以，从测量的到的状态方程的数据，或者从状态方程模型比如理想气体方程,范德瓦尔斯方程或者其他状态方程,我们就可以知道。
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for real gases. This is an equation of state for an ideal gases.
我们需要描述实际气体,的状态方程。
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So again, if you do a calculation where you're close enough to the ideal gas and you need to design your, if you have an engineer designing something that's got a bunch of gases around, this is a useful thing to use.
要研究近似理想气体的表现时,这个方程非常有用,下面再来看一个，对我们来说最有意思的,实际气体状态方程：,范德瓦尔斯方程。
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pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
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Remember the equation of state for Van der pV=nRT Waal's gas is not pV is equal to nRT, but p plus the attraction term.
记住范德瓦尔斯气体的状态,方程不是，而是p加上一个吸引项。
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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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nRT So, dp/dT, for our ideal gas, at constant volume, remember pV is nRT.
对于理想气体状态方程pV等于，所以对理想气体。
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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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T It's just equal to V over T.
把气体状态方程代入得到V除以。
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