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I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了，因此可以用,理想气体状态方程消去。
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If gas is expensive, then we can't take a road trip.
如果汽油很贵的话，我们就没法开车旅行。
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And if you put this in the well-ventilated area, if you prepare this outside, the h c n gas will actually be released into the air, so you're safe, you can eat it later.
而如果你把它们放在通风良好的地方，在室外处理，那么氰化氢气体,将会被释放到空气中，这样你就安全了，过后就可以吃了。
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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△
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So we are really looking at this reaction here H+ for ionization. It is H gas neutral goes to H plus in the gas phase plus the electron. And, furthermore, we can have multiple ionization energies.
所以我们真正看到的是,电离，它是在气相中H变为,和电子的过程，还有，我们能电离能加倍。
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If gas is cheap, then we can go anywhere we want.
如果汽油很便宜的话，我们想去哪里都可以。
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And we can maybe share the cost of the gas together.
我们也许可以平摊油费。
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Then I can go back, the gas is included at every point of the way.
我就能走回去，气体被包含在路径上的每个点中。
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They're very deep and held very tightly to the nucleus, so we can often lump them together and instead of writing them all out separately, 3s1 we can just write the equivalent noble gas that has that configuration.
它们非常深,被原子核吸得很紧，所以我们通常可以把它们混在一起,而不是把它们写开，我们可以写出氖然后3s1所以,或者任何的一个。
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If you have a real gas and you write du is Cv dT and your path is not a constant volume path, then you are making a mistake. But for an ideal gas, you can always write this. And this turns out to be very useful to remember.
对于真实气体，如果其变化过程,不是恒容的，du=Cv*dT就不成立，但对于理想气体,这条规则永远成立,这一点非常有用，请记住。
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You take your room temperature liquid helium and you cool it with liquid nitrogen to 77 degrees Kelvin, the new, you're not quite there yet 77k unfortunately right? Then you take hydrogen you cool it would liquid nitrogen to 77, then you can use your hydrogen gas.
首先要有常温的氦气,拿液氮把它冷却到77k，那个新来的7,你不坐在那儿，对吧？,然后用液氮把氢气降温到,然后就可以使用这个氢气了，想要用氢气来做焦耳-汤姆孙实验。
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We can go all the way down -- magnesium aluminum, all the way to this noble gas, 3s23p6 argon, which would be n e and then 3 s 2, 3 p 6.
我们可以继续，镁，铝,一直到惰性气体，氩它是Ne然后。
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RT So it's delta u plus RT, we can say T1 is the n temperature we've used here, delta n of the gas.
所以它应该是ΔU加,我们可以在这里用T1，气体的Δ
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Or, if we know the equation of state from a model, ideal gas, van der Waal's gas, whatever, u now we can determine u.
或者如果我们知道模型的状态方程,比如理想气体，范德瓦尔斯气体，无论什么，我们就可以利用状态方程得到内能。
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You've just done an adiabatic compression of the ideal gas, you can pretend there is an ideal gas.
这就是对理想气体的,绝热压缩，---我们把空气近似作为理想气体处理。
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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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