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It's true for any gas, and if I remove this limit here, r t is equal to p v bar, I'm going to call that an ideal gas.
这样的气体被称作理想气体,这就是理想气体的性质，理想气体的涵义是什么？
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So instead of v bar, we write p v bar minus b, equal r t.
现在考虑，这些气体分子之间。
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V So this nR over V. And then, using the relation again, T we can just write this as p over T.
恒定温度下的dp/dT等于nR除以，再次利用状态方程，可以把它写成p除以。
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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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T p V I've got three variables, T, p and V.
一共有三个变量：
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Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.
一般情况下我不能这么写,因为这一项会包含pdV和，但是我们已经假定压强为常数，所以包含dp的部分等于零。
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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v We don't know what it is yet. In order to change this from a p to a V, you have to use the chain rule. So let's use the chain rule.
为了把这里的p变成,我们需要利用链式法则,好，让我们使用链式法则。
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We want a relationship in p-V space, not in T-V space. So we're going to have to do something about that. But first, it turns out that now we have this R over Cv.
我们想要p-V空间中的结果，而不是T-V空间中的,因此需要做一些变换，先来看现在的关系，它跟R/Cv有关。
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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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STUDENT: from the T delta V p to the delta p here?
学生：,从TΔV到这里的Δ
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That's where that term comes from, du/dV dV/dT.
乘以偏V偏T，p恒定，这项的来源。
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Only V, p and T appear.
只有体积V，压强p和温度T出现。
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