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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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And typically, we'll be treating at least some cases where we're dealing with ideal gases in which case we can easily get delta u.
那么我们也可以定出功，对吧？,典型地，我们至少会处理,一些理想气体的情况。
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So let's take our one model that we keep going back to Equation of state, and just see how it works.
我们回到经常使用的理想气体模型,或者说状态方程。
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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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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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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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For real gases, there's a whole bunch of equation the states that you can find in textbooks, and I'm just going to go through a few of them.
这是理想气体的状态方程,对实际气体,你可以在教科书里，找到许多描述它们的,状态方程。
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And again there, too, you saw an experimental result you were presented with that says, well at least to the extent that it could be measured, it was obviously getting very small.
再一次，你看到了一个,你经知道的实结果，至少在实验测量的范围内，对理想气体条件下的气体这一项很小。
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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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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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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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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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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 I have this adiabatic expansion where p external is really small.
这时的情况,跟理想气体的。
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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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So from measured equation of state data, or from a model like the ideal gas or the van der Waal's gas or another equation of state you know this.
所以，从测量的到的状态方程的数据，或者从状态方程模型比如理想气体方程,范德瓦尔斯方程或者其他状态方程,我们就可以知道。
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All right, so gamma is for ideal gas, 1 is bigger than one.
对理想气体，γ大于。
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