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OK, this is only true for an ideal gas, and we went through that mathematically where the, with a chain rule.
这一关系只对理想气体成立，上节课我们,用链式法则推导出了这一关系。
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Let's try it with a different equation of state, that isn't quite as simple as the ideal gas case.
考虑一个不同的状态方程，这状态方程不像理想气体状态方程那么简单。
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The last time you saw that for an ideal gas, the energy only cared about the temperature.
上次你们知道了，理想气体的能量只与温度有关。
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This needs to be stressed that this is the ideal gas case. Now regular gases, real gases fortunately as I said, don't obey this.
需要强调的是这是对理想气体而言的,普通气体，真实气体，就像我说过的,不遵循这个规律，这是非常重要的。
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Now, we saw before, or really I should say we accepted before, that for an ideal gas, u was a function of temperature only.
我们已经看到,或者说我们已经接受这样一个事实，即理想气体的内能只和温度有关。
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That for an ideal gas it has to be the case that there's no volume dependence of the energy.
我们可以直接推导这个结果,即证明对理想气体，内能和气体体积无关。
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Your plant is going to blow up, because the ideal gas law works only in very small range of pressures and temperatures for most gases.
理想气体定律,只在一个很小的压强,与温度的范围内适用。
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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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PROFESSOR BAWENDI: So the question was, for an isothermal expansion, delta u does not change, therefore, The answer is that's true only for an ideal gas.
你的问题是，在等温过程中，内能是否，这只对理想气体成立。
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And the temperature scale that turns out to be well-defined and ends up giving us the concept of an absolute zero is the ideal gas thermometer.
比如理想气体温标,它有精确的定义,并能引出绝对零度的概念,今天我们就先来谈谈它。
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You're allowed Cv comes out here for this adiabatic expansion, which is not a constant volume only because this is always true for an ideal gas.
绝热过程写下,这个式子是因为它对理想气体都成立，并没有用到等容过程的条件,只用了理想气体的条件。
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H for an ideal gas is only a function of temperature. This is not true for a real gas fortunately, but it's true for an ideal gas.
不正确的,但是幸运的是,对于理想气体是完全正确的。
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B=0 There's going to be some temperature where B is equal to zero. In that case, your gas is going to look awfully like an ideal gas.
在某个温度,这时，实际气体的表现，十分接近理想气体,高于这一温度它是正的。
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This quantity is exactly zero for an ideal gas and we'll discover why eventually it has to do with what we mean by an ideal gas it turns out.
对理想气体它是零,这点我们接下来会知道是,为什么，这与为什么我们叫它理想气体有关。
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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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PROFESSOR BAWENDI: So, for an ideal gas, the isothermal is the easy one because the energy doesn't change.
对理想气体，等温过程最简单,因为能量不变。
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Great. So now we have this ideal gas thermometer, and out of this ideal gas thermometer, also comes out the ideal gas law.
好，现在我们有了理想气体温度计,由此还可以引出理想气体定律，我们可以得到这条，插值出的直线的斜率。
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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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So that you could see that for the ideal gas, u would not be a function of volume, but only of temperature.
所以我们可以看到对理想气体，内能不依赖于体积，而仅仅是温度的函数。
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So for an ideal gas, we saw that u was only a function of temperature.
对于理想气体，我们知道内能只是温度的函数。
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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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All right, next time we're going to talk about a much better scale, which is the ideal gas thermometer and how we get to the Kelvin scale.
好，下次我们,会讲一种好得多的温标，关于理想气体温度计,和开氏温标的导出。
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It's true for any gas, and if I remove this limit here, r t is equal to p v bar, I'm going to call that an ideal gas.
这样的气体被称作理想气体,这就是理想气体的性质，理想气体的涵义是什么？
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In other words, we're taking advantage of the fact that we now know that quantity. In the case of the ideal gas we just have a simple model for it.
换句话说，我们可以利用我们已经,了解这个物理量的这个优势,对理想气体我们有一个简单的模型。
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And if that's equal to zero, that means that the Joule-Thomson coefficient for an ideal gas is also equal to zero. We're going to actually prove this later in the course.
说明理想气体的,焦耳-汤姆逊系数也等于0。,详细的证明过程,会在以后的课上给出。
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And now we're going to specify, we're going to do a Carnot cycle for an ideal gas.
我们具体地指定一个卡诺循环，这是理想气体。
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So for an ideal gas then, dH/dp under 0 constant temperature, that has to be equal to zero.
所以对于理想气体,偏H偏p在恒温下，等于。
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And we saw that, you saw that the Joule coefficient for an ideal gas was zero.
我们会发现，你们也会发现,理想气体的焦耳系数是零。
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And that's because this is different from what it is in the ideal gas case.
因为这一项,和理想气体中的对应结果不同。
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But this is only true for an ideal gas and it's approximately true for other things.
但这只对,理想气体城里。
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