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So what we've discovered from this relationship dq that du at constant volume is equal to dq v.
从这个关系式里我们发现,恒体积时的du等于恒体积时的。
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A It tells me that the partial of A with respect to T at constant V is minus S. Right?
他告诉我们,在恒定体积下对温度的微分等于负S，对吗？
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Why is that? Because w and v are constant.
为什么？因为w和v是常数。
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Whenever you see a particle moving in a circle, even if it's at a constant speed, it has an acceleration, v square over r directed towards the center.
只要看到质点做圆周运动,即使是匀速圆周运动,也存在一个加速度,大小为 v^2 / r,方向指向圆心
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So the first path then, the first path, 1 constant volume constant V, so I'm going to, again, let's just worry about energy.
首先，是路径，等压过程。
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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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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.
一般情况下我不能这么写,因为这一项会包含pdV和，但是我们已经假定压强为常数，所以包含dp的部分等于零。
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So we immediately get du at constant S and V is less than zero.
这样我们马上就得到以下结论：,在等熵，等容条件下dU必须小于零。
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V All right, or p is equal to a constant divided by volume.
或者p等于常数C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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And so now we have this quantity, p times v bar, and the limit of p goes to zero is equal to a constant times the temperature.
不仅仅对氢气或氮气适用，在p趋于0的极限下,它适用于任何气体。
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take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.
对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r
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Well, we already know what dA/dT at constant V is.
我们知道恒定体积下的。
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v du/dV under constant temperature. du/dT v under constant volume. You use the Joule expansion to find these quantities.
像偏u偏v，恒温下的偏u偏,恒容下的偏u偏,你们知道怎么运用焦耳定律。
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This depends on the path. It tells you right here the path is constant pressure. These don't depend on the path, right. V doesn't care how you v get there. u doesn't care how you get there.
这由变化的具体路径决定,这个小脚标表明过程是恒压的,这些量都与具体路径无关,即不管是通过什么路径使得体积变化为Δ
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SV And this is, of course, with constant S V.
当然在这里是保持恒定的。
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Then you take p1 to p2 with V constant.
图上画出来就是这样。
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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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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