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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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I'm going to do something which somehow we are told never, ever to do, which is to just cancel the dts.
我接下来要做一件以前绝对不允许的事情,约去这些dt
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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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So, we do an integral over a path, dT for the heat capacity along that path, dT.
因此，我们沿着路径做一个积分，热容。
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So if you get these two guys together you get CvdT=-pdV Cv dT is minus p dV.
把它们联系,起来。
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du, it's an ideal gas. So this is Cv dT and of UB course we can just integrate this straight away.
因此这是CvdT，当然我们可以,直接算出这个积分，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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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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dT This is equal to Cp minus R dT.
等于。
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dG/dT That is, this is, dG/dT at constant pressure.
这就是恒定压强下的。
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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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p So dV/dT at constant pressure is just nR over p.
所以恒定压强下dV/dT等于nR除以。
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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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So you are supposed to know, for example, if x is t^, you're supposed to know dx/dt is nt^.
接下来你就会知道,例如,如果x=t^,那么dx/dt=nt^
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dV OK, so we've got dT here dV here.
等式的左边是dT，右边是。
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And so that means that delta u is always calculable from Cv dT for any ideal gas change.
这意味着对理想气体,Δu只需利用Cv，dT计算。
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And I know pdV what those turn out to be. It's minus S dT minus p dV.
我们知道,这最终就是负SdT减去。
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Now you have to know from elementary calculus that v times dv/dt is really d by dt of v square over 2.
根据初等微积分知识你们得知道,v乘以dv/dt其实就是d/2)/dt
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/T We've got Cv integral from T1 to T2, dT over T is equal to minus R from V1 to V2 dV over V.
左边是Cv乘以，从T1到T2对dT积分。
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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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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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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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So we have dH/dT keeping pressure constant, is du/dT keeping pressure constant.
等于偏U偏T，p恒定加上，偏pv偏T，p恒定。
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SdT So we have dA is minus S dT minus T dS.
我们得到dA等于负TdS减去。
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SdT So dG is dH minus T dS minus S dT.
所以dG等于dH减去TdS再减去。
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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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dT That means that dH is also equal to dH/dT, constant pressure dT. All right, so now I've T ot more dH/dT under constant pressure.
也等于偏H偏T恒压乘以，现在我已经得到了在恒压,状态下的偏H偏。
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pdV Minus S dT, that's the p dV term that's left, minus p dV.
应该是负SdT，留下的应该是pdV项负的。
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