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dT/dp is mu JT. So for a real gas like air, this is a positive number. It's not zero.
所以对于像空气这样的真实气体，这是一个正数，不等于零。
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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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If T is less than T inversion, you have the opposite case, and dT/dp is greater than zero.
如果T比转变温度低,情况就相反，偏T偏p大于零。
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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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So for an ideal gas then, dH/dp under 0 constant temperature, that has to be equal to zero.
所以对于理想气体,偏H偏p在恒温下，等于。
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So then, just like we saw, analogous to what saw just before, dS/dp it's T dS/dp at constant T.
就像我们看到的,就像我们刚才看到的一样，结果是T乘以恒定温度下的。
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dG/dp And this is dG/dp at constant temperature.
这是恒定温度下的。
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p This is going to get us dH/dp constant temperature. What is this experiment?
这帮助我们理解恒温条件下的偏H偏,那么这个实验具体是什么呢？
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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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In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
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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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Vdp So dH is just du plus p dV plus V dp.
所以dH等于du加上pdV再加上。
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Therefore, from experiments, u is only a function of temperature for an ideal gas, H and therefore from these experiments, 0 we come out with delta H dH/dp is equal to zero.
因此，从实验可以得出,对于理想气体u只是温度的态函数，因此从这些实验中我们得到Δ,偏H偏p等于。
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What is dH/dT as a function, keeping pressure constant, what is dH/dp, keeping temperature constant?
恒定时偏H偏T是什么,温度恒定时的偏H偏p又是什么呢？,好的，让我们解决第一个问题？
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d2G/dpdT So d squared G dT dp is equal to d squared G dp dT.
所以d2G/dTdp等于。
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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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So we already know that. So now we can write CpdT or differential dH as Cp dT plus dH/dp, pdp constant temperature, dp.
我们已经知道了这个，所以我们现在,可以写出H的微分式：dH等于，加上恒温时的偏H偏。
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Vdp So dG is minus S dT plus V dp.
结果是dG等于负SdT加上。
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OK, so now we have the other one, p dH/dp constant temperature.
好的，现在我们来研究另一个量，在恒温条件下的偏H偏。
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So if you had a high temperature, this a small compared to b. If you're negative which means that dT/dp at constant H is less than zero.
高于反转温度，这一项相比于b很小,意味着H恒定时,偏T偏p小于零。
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T Remember, we're trying to get delta H, p we're trying to get dH/dT constant pressure and dH/dp constant temperature. OK, these are the two things were trying to get here.
想要得到在恒压状态下的偏H偏，和在恒温状态下的偏H偏,好的，这是两个我们，在这里想要得到的东西。
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dT/dp is positive. dT/dp is positive.
偏T偏p是正数，好的这就是。
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JT dT/dp is positive, well that's mu JT.
偏T偏p就是μ
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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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