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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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We start at p1, V1. and p external is equal to zero.
从状态开始，外部压强为零。
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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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So this guy here gets rid of this, and I have my answer as V1 over V2 to =p2/p1 the gamma power is equal to p2 over p1.
这两项抵消掉了，于是等式,变成了^γ
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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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There's p1 here, and p2 here So I'm starting at p1, V1. I'm starting right here And I'm going to end right here.
它的分子间作用力很小,十分接近理想气体,对它做一个压缩过程。
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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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V2/V1 There's a V1 over V2 here or V2 over V1.
这边是。
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log So that's just the log of V2 over V1.
因此就是。
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p1 V1 OK, so in my diagram now, I have p1, V1 for my gas.
于是可以画出现在的p-V图。
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w=p1v1 So we write down p1, V1.
我们写下。
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There is V1 here. There's V2 here.
比如说氩气。
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OK, now we actually would like to simplify this or to write this in terms of not the volume change, v2/v1 but the pressure change. So, we have V2 over V1.
接下来我们将要把问题简化,不用体积变化来描述，而改作用压强变化来描述，现在我们有。
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And if I draw a diagram on a T-V diagram of T-V V1 I'm starting with some V1 here.
画出过程的,图，what，I’m，doing，here，初态是。
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v1=/p1 So V2 = /p2, and V1 = /p1.
因此v2=/p2，同样地。
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v1 So we have p1, V1. We have stops.
内部气体压强为p1，体积为。
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p2 There is going to be an internal pressure where T1 p1 is less than p2 and there's V1 and T1 here.
内部气体压强p1小于,体积为V1，温度为。
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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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w This is just q plus w. There's w, RT1 ln q has to be R T1 log of V2 over V1.
而U等于q加，那是w，q应该是。
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We can combine these two to see V2 that V4 over V1 must equal V3 over V2.
我们把这两个结合起来,得到V4除以V1等于V3除以。
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I'm pressing on the gas. So I expect that to be a positive number. The pressure is constant 0 p. The V goes from V1 to zero.
我们对气体加压,所以这应该是一个正数,压强是常数，p，V从V1变成。
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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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V1 This first integral is zero V1 to V1, then I get minus p2 times V2 minus V1 or p2 times V1 minus V2. Again, 0 a positive number.
先保持体积为，对pdV积分1,然后对p2dV从V1到V2积分，第一部分积分为。
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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 any point I pick on that path will be equal to p1, V1 to the gamma.
也就是说路径上面任取一个点,计算p，V^γ
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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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Let's take a system. Under constant pressure T1 V1, going to a second -- this is the system, so let me write the system here.
我们建立一个系统1,在恒定的压强T1，V1，下，变成了另一个系统，-这个初始的系统让我把它写在这。
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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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