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So, so far we don't have a way to just write off, relate them to equation of state data.
到目前为止我们还没有办法，写出他们和状态方程之间的关系。
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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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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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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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This is going to be probably a homework at some point to do this. For now, let's take it for granted. Let's take it for granted that we know how to calculate this derivative from an equation of state like this.
这可能是将来的一个课后作业,现在，请把这当成理所当然的，理所当然地认为我们,知道怎样从一个状态,方程计算这样的微分式。
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You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
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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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And the beauty of that equation of state is that it only relies on two parameters.
范德瓦尔斯方程,先把结果写出来。
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Now, the most interesting one for our class the equation of state that's the most interesting, is the Van der Waals equation of state, developed by Mr. Van der Waals in 1873.
由范德瓦尔斯在1873年发展起来,这个方程的美妙之处，在于它只需要两个参数，下面我们来研究一下。
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So that's one example of a real equation of state.
第一个例子。
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Because this is what comes directly out of an equation of state, right?
因为它,可以直接从状态方程中得到？
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And again, this is something that comes from an equation of state.
我们再一次发现,这个可以从状态方程中得出。
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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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Again, if we know the equation of state, we know all this stuff.
如果我们知道状态方程，我们就可以知道所有的物理量。
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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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Well, then, we could just use that for our equation of state.
然后我们就可以把这些数据,作为我们的状态方程。
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Of course, that's assuming we know the equation of state.
这意味着我们假定,我们知道其状态方程。
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From equation of state data. Terrific, right?
非常好，不是吗？
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So again, we can measure equation of state data.
我们可以通过测量得到状态方程的数据。
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This is called an equation of state.
这一状态方程把压强。
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So that's an equation of state.
所以它是态函数。
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That's what the equation of state tells us.
这是状态方程告诉我们的。
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So now, this equation here relates three state functions together: the pressure the volume, and the temperature. Now, if you remember, we said that if you had a substance, if you knew the number of moles and two properties, you knew everything about the gas.
压强，体积和温度,大家应该还记得,我们提过，只要知道气体的摩尔数,和任意两个状态函数,就可以推导出其他的状态函数，这样，我们可以把它改写成。
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Just like u, we'd like to be able to express it in a way that allows us to calculate what happens only from equation of state data.
就像内能u一样，我们希望能够利用状态方程的数据,计算出其表达式,这些表达式能方便我们说出即将发生的过程。
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So we'd really like to be able to find some sort of equation of state, or some sort of rather function of state that's going to relate the heat going in or out of the system with that function of state, because this isn't going to do it.
所以我们真的想要去,找到一些态方程或者态函数,通过这个态函数可以表示热量,在系统与外界的交换,因为这个不能表示它。
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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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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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b Let me just first write it down, the Van der Waals equation of state.
有两个参数，a和，如果a和b等于0的话。
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OK, in a few weeks, you're going to find out that we can calculate dH/dp from this equation of state, and you're going to find p out that dH/dp from that equation of state b-a/RT is proportional to b minus a over RT.
好，在接下来几个星期里,你们将知道从这个状态方程,可以计算出偏H偏p，并且你们会发现,从这个状态方程得到的偏H偏,正比于。
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