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For a real gas it depends on more than the temperature STUDENT: Are there any other constraints similar to that .
而对实际气体，这是不对的,它的内能不仅仅依赖于温度,学生：有其他,类似的约束吗？
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You told me that you'd be here in 10 minutes.
你还说十分钟内能到达的。
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And the bigger lesson from that is that entropy, unlike energy u or enthalpy H, we could define an absolutely number for it.
热力学第三定律的一个更重要的推论是,与内能和自由焓不同，我们可以给上定义一个绝对的数值。
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It is essentially equal to internal energy for condensed systems, but when you look in the books sometimes they will use this term.
它与内能是相同的,在凝聚体系中，在你看书时有时你会发现,它们会这样使用。
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When we measure EKG's, what we're measuring is the activity of all these cells within our heart performing action potentials.
当我们做心电图的时候,我们所测量的是心脏内能发出,动作电位的细胞的活动状态
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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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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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For isothermal expansion, that means that delta u does not change, but delta q is equal to delta w?
在等温过程中，是不是内能不变，Δq等于Δw？
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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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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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So, I just want to write a few examples down with a few values for delta u or delta H or delta S, and see whether we can get any clues from what we see.
我先写一些例子,例子包含一些内能，自由焓和熵的变化数值，然后看从中,我们能不能得到一些启示。
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But it's allowed to say the internal energy is a function of temperature and volume.
但是我们也可以说内能,是温度和体积的函数。
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So, we have, we're interested in the change in internal energy for various experimental constraints.
我们感兴趣的是,在各种实验环境约束下内能的改变。
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Do we calculate, you know, delta S, delta u, delta H?
是否要计算熵的变化，内能的变化，自由焓的变化？
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One is, du, u is called the internal energy dw or just the energy, is equal to dq plus dw.
其中一个是：du，u是内能,或能量，等于dq加上。
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When you say that, it implies that the differential is given by this pair of partial derivatives.
这就意味着，内能的微分,等于偏u偏T，保持体积不变。
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And so for many, many problems, especially on exams, especially on this first exam, you will be able to say that this is the relationship between internal energy and temperature.
对于很多问题，特别是考试中的问题，你们要能够说出来,这是内能与温度的关系。
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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There's an interplay between the energy inside the gas which is the heat energy which is allowing me to do all that work to be outside, and so I'm using up some of the energy that's inside the gas to do the work on the outside.
即使没有热传递,能量也能以,做功的形式传递出去，气体的一部分内能,转化成了功。
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The value of the internal energy is only determined by temperature.
内能的值,只与温度有关。
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And the first law says, well heat and work are different forms of energy, and we can add them, and the path dependence of these two things is somehow cancelled in the fact that we have this internal energy.
热力学第一定律说，热和功是能量的不同表现形式，我们可以把它们加起来,它们与路径相关的部分相互抵消,我们就有了内能。
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That u is a function of temperature only.
内能只是温度的函数。
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We discovered that the quantity dA, under conditions of constant volume and temperature, dA TS And A is u minus TS.
我们发现在恒定的体积和温度下，亥姆赫兹自由能的变化，小于零，is，less，than，zero。,亥姆赫兹自由能A等于内能u减去。
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Now I make the volume bigger.
一些内能，把体积扩大。
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So dS for u and V fixed is greater than zero.
所以当内能u和体积V固定时，dS大于零。
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Where the Gibbs free energy, TS u plus pV minus TS is H minus TS.
吉布斯自由能等于，内能u加上pV减去TS，也是自由焓H减去。
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pV So our H is u plus pV, as you know.
我们的自由焓H等于内能u加上。
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And u is minimized at equilibrium.
这说明平衡状态下内能u是最小的。
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TS A is u minus TS.
亥姆赫兹自由能A等于内能u减去。
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