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pV=RT dT here because the pressure is constant, dV=RdT/p so dV is equal to R over p dT.
因为对1摩尔气体有，于是。
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P dV is equal to R dT. pV = RT for 1 mole, pdV=RdT so I just take dV here.
对等压过程，那么。
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dU=CvdT pV=RT So I can write du is Cv dT and pV is equal to RT.
于是。
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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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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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I'm going to call it r. It's going to be the gas constant, and now I have r times t is equal to the limit, p goes to zero of p r.
如果去掉p趋于0的条件,在有限压强下都,保持RT=pV的关系。
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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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RT So it's delta u plus RT, we can say T1 is the n temperature we've used here, delta n of the gas.
所以它应该是ΔU加,我们可以在这里用T1，气体的Δ
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RT/V this expression becomes Cv dT over T is equal to CvdT/T=-RdV/V minus R dV over V.
这样，or，RT，over，V，bar。，So，now，这个等式就,可以化成。
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Now if you're at the temperature which is b higher than the inversion temperature, in that case here, a over RT is small compared to b, and this is going to turn out to be negative.
T>Tinv】,这时a/bR小于,结果是负数，因此如果温度。
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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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V RT over V.
因此等于RT除以。
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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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