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Cv+R=Cp Cv is equal, oh Cv plus R is equal to Cp it's a relationship that we had up here that we wanted to prove.
我们就得到了,我们一开始,想要证明的。
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Cp, I forgot to put my little bar on top here because it's per mole Cp dT that's my dq here.
上面的Cv我忘记加上横线了,因为它也是摩尔热容。
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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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Cv So, for Cp and Cv, these are often quantities that are measured as a function of temperature, and one could, in fact, calculate this integral.
一般Cp和,都是温度的函数，因此实际上，我们可以将这个积分计算出来。
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By definition I'm going to define gamma by Cp over Cv by definition.
把Cp/Cv记作γ,这完全是定义。
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T So we know that T dS/dT at constant volume is Cv over T, T and dS/dT at constant pressure is Cp, over T.
在恒定压强下定压比热容Cp乘以dT除以,所以在恒定体积下dS/dT等于Cv除以，在恒定压强下dS/dT等于Cp除以。
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T It's Cp dT over T at constant pressure.
定容比热容Cv乘以dT除以。
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UC So we can immediately write delta u C is Cv times T1 minus T2. Delta Hc C is Cp times T1 minus T2, right?
所以我们可以直接写出△,是Cv乘以,△HC是Cp乘以，对吧？
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This is only true for an ideal gas. Since it's true for an ideal gas, then we can go ahead and replace this with Cv, and then we have Cp=Cv+R Cp with Cv plus R, which is what we were after.
常犯的一个错误，这只对理想气体成立,因为对理想气体成立,所以我们可以继续，用Cv代替,这项，最后得到。
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There I have it Cp is equal to Cv plus R, right?
所以Cp=Cv+R，对吗？
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Cv What do we know about the Cp and Cv?
关于Cp和？
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Cv The only difference is it'll be Cp instead of Cv, B but there it is for pathway B. There it is for C a pathway C. So the state functions that we're familiar with are doing what we expect they ought to be doing, right? If you go around in a cycle, starting and ending at the same place the state functions have to stay the same.
是Cp而不是，这是路径,这是路径,所以我们熟悉的态函数的行为,正与我们预期的相同，对吧？,如果你沿着循环走一圈,开始和结束于同一个位置。
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