R/Cv OK, so that means that this is really instead of -1 R over Cv. it's really gamma minus one.
现在,变成了γ
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△
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。
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。
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。
Here's heat exchanged in pathway A and in pathway B heat is zero, and in pathway C, Cv here is qC it's Cv T1 minus T2.
这是qA,这是路径A上的热量交换,路径B中的热量交换是零,而在路径C中,这是qC,它是。
In B it isn't, it's Cv times T2 minus T1, right.
在B中不是,而是Cv乘以。
T It's Cp dT over T at constant pressure.
定容比热容Cv乘以dT除以。
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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