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So now if I look at my V1 over V2 to the gamma minus 1, that's T2 over T1.
于是把^=中2,的两个温度。
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So, the first obvious one is to take V1 to V2 first with p constant. So take this path here.
从初态到末态可以有无数种路径2,甚至像这样，我们只研究两种。
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Argv2 Let me go ahead and now run Arg V2 with nothing.
我们现在继续运行。
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You might have already noticed that I'm using the classes V2 server so the syllabus is there, I'm going to go over the syllabus a little bit later, but the syllabus is available online.
你们可能已经注意到,我使用了班级服务器,所以课程大纲在这儿,虽然我待会儿会把这页内容翻过去,不过课程大纲已经挂在网上了
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If you,or a friend of yours,wants to see this syllabus after the class,and you don't have one, it's on the Classes v2 server.
如果你或你朋友想在课后看看,但你没有多余的，可以在Classes，v2服务器上找到。
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I put it up on the ClassesV2 not as part of the reading list but it's under Resources so you can read Kipling.
我把它放到V2类别2,并没有放到阅读列表里,而是在“资源“里，所以你可以阅读吉卜林的作品。
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V3 Here's the V4 over V3, V1 oops, sorry. V2 over V1, this is equal to the inverse of this.
所以就是这里的V4除以，哦，对不起，V2除以，它是它的倒数。
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p2 So they're both p2. external is p2 p2 V2 T2 and I have p2, V2, T2, on the other side.
都是2,这样末态是。
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I'm going from V2 to V2 dv - what do you think this integral is? Right, W1 so this is easy part, zero here.
这样才保证了过程的可逆性,下面来计算，路径1的功。
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V2 Now we could put stops here at V2, but this piston would just kiss the stops.
现在我们可以把挡板放在这里，这时体积是，活塞会刚好碰到挡板。
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Every time you do the experiment T in equilibrium with the heat bath at T, v2 you'll get the same p2 and V2.
与热库相接触的每次实验中,达到热平衡后的温度都是，压强都是p2，体积都是。
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log So that's just the log of V2 over V1.
因此就是。
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V2 You could also do a different path.
再保持体积为。
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And so we can write this, ln minus nRT log V2 over V1.
所以结果是，负的nRT除以。
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I take V1 to V2 first, keeping the pressure constant at p1, then I take p1 to p2 keeping the volume constant V2 at V2. Let's call this path 1.
容易计算的路径，第一条路径，是首先保持压强不变,体积从V1压缩到。
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V2 p1 times V2 minus V1. What that turns out to be, 0 this area right here. It's V1 minus V2 times p1.
第二步做的功是-pdV，积分从V2到，这部分积分出来是多少？应该是。
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The ideal gas constant doesn't change, temperature doesn't change, and so v we just have minus nRT integral V1, V2, dV over V.
理想气体常数不变，温度也不变，因此,是负的nRT，积分从v1到v2，dv除以。
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So, the work for this process is the integral, pdv or minus the integral, V1, V2, p dV.
此过程中的做功等于负的积分，从v1到v2，外部。
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So on the p-V diagram, then, V1 V2 p1 p2 there's a V1 here a V2 here, a p1 here a p2 here.
在p-V图上，这是。
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So it's nR integral from V1 to V2 dV over V.
即nR除以V乘以dV从V1到V2的积分。
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p1 V1 Initial find -- there are many ways p2 V2 V1 I can get from one state to the other.
初态的氩气状态为,末态为。
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V2 So, if one goes to two and V1 goes to V2, and it's constant temperature, just what we've specified there.
如果状态1变到状态1并且体积从V1到，同时温度保持不变，这就是我们这里要讨论的问题。
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meke Argv2 So this is make Arg V2.
那么。
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so we know how to do this, and we know this thing when it hit these stops, v2 the pressure with p2, and the volume was V2.
所以我们知道怎么计算，当活塞到达这两个挡板时，压强是p2，体积是。
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p1V1/R That p2 V2 over R, and then I have p1 V1 over R, the R's cancel out.
就是p2V2/R除以，两个R消掉了。
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Remember it's the external pressure that's important. In this case, because it's a reversible process, the external pressure turns out to be always the same as the internal pressure.
是过程非常缓慢,比如我把体积，从V1压缩到V2时，我做得十分缓慢,在过程中的任何一点。
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v dv We have minus V1, V2, nRT over V dV.
负的v1，v2，nRT除以。
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So now let's try looking at something V2 where are V1 goes to V2.
现在我们考察一个过程,这个过程中系统的体积从V1变到。
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p1 An isobaric process followed by V2 a constant volume process.
先保持压强为,体积从V1压缩到。
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V1 to the gamma is equal to p2 V2 to the gamma.
就是，p1，V1^γ,等于p2，V2^γ
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