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dU=CvdT So du is still going to be equal to Cv dT, and we're still going to be able to use the first law, all these things don't matter where the path is.
于是，第一定律也依旧成立，这些关系都与路径无关。
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So we can now take this expression and rewrite it under the condition of du is equal to zero.
我们利用这个公式,并在du=0的条件下将它重写。
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I suggested that there was a critical response to those issues that was somewhat negative, and I want to sort of remind you of that from W. E. B. Du Bois's review of Black Boy when it came out.
对于负面问题,有个关键评述，大家看一下,关于《黑孩子》的评论。
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dq=0 But if it's adiabatic, then dq is equal zero, du=dw and for an adiabatic process, then du is equal to dw.
但如果它是绝热的，那么，因此对于绝热过程。
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It's constant pressure. OK, so now, last time you looked at the Joule expansion to teach you how to relate derivatives like du/dV.
这是恒压的，好，上节课你们,学习了焦耳定律,以及怎样进行导数间的变换。
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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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dU=dq+dw Well from the first law, du is equal to dq plus dw, and I wrote down everything I knew at the beginning here.
第一定律“,前面我们已经,看到了。
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So what we've discovered from this relationship dq that du at constant volume is equal to dq v.
从这个关系式里我们发现,恒体积时的du等于恒体积时的。
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One is, du, u is called the internal energy dw or just the energy, is equal to dq plus dw.
其中一个是：du，u是内能,或能量，等于dq加上。
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du So, we can also write delta u as integral from 1 to 2 of du.
我们也可以将Δu写成,从1到2的积分。
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du=0 So that implies du is equal to zero.
因此。
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v du/dV under constant temperature. du/dT v under constant volume. You use the Joule expansion to find these quantities.
像偏u偏v，恒温下的偏u偏,恒容下的偏u偏,你们知道怎么运用焦耳定律。
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but right now you're going to have to take it for granted. So, if the Joule-Thomson coefficient is equal to zero, just like we wrote, du = Cv dT du = Cv dT for an ideal gas, we're going to dH = Cp dT have dH = Cp dT for an ideal gas as well.
但是现在请你们应该把它看成理所当然的,所以，如果焦耳-汤姆逊系数等于零,就像我们写的，对于理想气体,我们也可以得到对于理想气体。
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We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.
我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。
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du It's an ideal gas, and that's equal to w1 prime.
等于CvdT，du，is，Cv，dT。,因为是理想气体，所以等于w1一撇。
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du=0 So du is equal to zero because dq and dw are both zero.
因此,因为dq和dw都等于零。
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So it would imply that CvdT du was equal to only the first term Cv dT.
这意味,这du进等于第一项。
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du/dT And we discover that du/dT at constant V T is equal to du/dT at constant V.
可以发现恒定体积下的,等于恒定体积下的偏u偏。
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Now, for an ideal gas, du/dV under =0 constant temperature is equal to zero.
对于理想气体，温度一定,时偏U偏V等于零。
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And so, we can immediately write this du and then we can write du for the universe, which is system plus surroundings is equal to zero.
因此，我们可以立刻写出这个等式,然后可以写出总的的，也就是系统加环境的du，等于零。
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And now we're just going to substitute du in here.
现在我们把上面的du的表达式代入。
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du But here you've got pressure constant. du, T this is du, not H here. du/dT is only equal Cv to Cv when the volume is constant, not when the pressure is constant.
这里是压强横笛，du，这是，不是H，偏U偏,只在体积恒定时等于，而不是压强恒定时。
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du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.
偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。
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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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du/dV under constant temperature was equal to zero for an ideal gas. And by analogy, we expect the same thing to be true here, because enthalpy and energy have all this analogy going on here. So let's look at an ideal gas.
偏U偏V在恒温下等于零,可以类比，我们希望在这里也一样，因为焓和能量有很强的类比性，让我们看看理想气体,【理想气体】
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