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That is, most processes that we're concerned with, they'll happen with something held constant like pressure or temperature or maybe volume.
这句话是说我们所关注的大部分过程，发生的时候都是保持某个量为常数,比如压强，温度或者体积。
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We could just collect a bunch of data. For a material .What's the volume it occupies at some pressure and temperature?
对一种物质我们可以得到一系列测量数据,在给定的温度和气压下,它的体积是什么？
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OK, now what we'd like to do is be able to calculate any of these quantities in terms of temperature, pressure, volume properties.
现在我们想要做的是能够利用,温度，压强和体积的性质,计算上面的物理量。
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On the other hand, temperature, volume and pressure are variables that are much easier in the lab to keep constant.
另一方面，温度，体积和压强,在实验室中比较容易保持恒定。
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And the equation of state, pressure versus volume at constant temperature, is going to have some form, let's just draw it in there like that.
系统的态函数，恒温下压强比体积，变化曲线，就像这样。
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For instance, the pressure and the temperature, or the volume and the pressure.
比如压强和温度，或体积和压强。
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There's a volume, there's a temperature, than the pressure here. There's other volume, temperature and pressure here, corresponding to this system here.
温度等状态函数有本质区别，这个状态有一组，确定的体积，温度与压强。
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So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
我现在所要做的一切就是,考察自由能对,温度，体积和压强的偏导数。
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And this volume, temperature and pressure doesn't care how you got there. It is what it is.
另一个状态,也有一组确定的体积。
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We know how the volume and temperature vary with respect to each other at constant pressure.
知道在恒定压强下,体积如何随着温度变化。
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You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
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You just need a few macroscopic variables that are very familiar to you, like the pressure, the temperature, the volume, the number of moles of each component, the mass of the system.
你只需要某些你非常熟悉的宏观变量,比如压强，温度，体积，每个组分的摩尔数，系统的质量。
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Now let's change the pressure and temperature and sweep through a whole range of pressures and temperatures and measure the volume in every one of them.
然后改变气压和温度,并且让气压和温度,取便所有可能的数值,测量相应的体积。
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In this case it relates the volume to the pressure and the temperature.
现在假想我们需要用,理想气体定律来设计一台机器。
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It relates the pressure, volume, and temperature together.
它把压强，体积，和温度联系在一起。
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In general, temperature and volume or pressure.
一般来说写成了温度，体积和压强的函数。
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That is, in real life, the variables that you'd normally control aren't some combination of entropy and these variables, but really their temperature, volume and pressure, any couple of those, might be what you'd really have under experimental control.
在生活中，我们所能控制的,不是熵和其他变量的组合，而是温度，体积，压强，以及其中的两两组合,这些才是试验中所能控制的。
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In this case, V = /P. Have two quantities and the number of moles gives you another property. You don't need to know the volume. All you need to know is the pressure and temperature and the number of moles to get the volume.
以及气体的摩尔数,就可以得到第三个量,知道压强，温度和气体的,摩尔数就可以推导出气体的体积,这称为状态方程,它建立了状态函数之间的联系。
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So now, this equation here relates three state functions together: the pressure the volume, and the temperature. Now, if you remember, we said that if you had a substance, if you knew the number of moles and two properties, you knew everything about the gas.
压强，体积和温度,大家应该还记得,我们提过，只要知道气体的摩尔数,和任意两个状态函数,就可以推导出其他的状态函数，这样，我们可以把它改写成。
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But because in many cases we can reasonably either model or measure equations of state, collect data for a material for its temperature, pressure, volume relations, then in fact if we can relate all these quantities to those then in fact we really can calculate essentially all of the thermodynamics. For the material.
但是因为在很多情况下,我们能够合理的给出状态方程的模型,或者通过收集一个物质的，温度，压强和体积之间的关系,来测量其状态方程，所以实际上我们可以给出压强等物理量,和热力学势之间的关系,并计算出所有的热力学势，对于给定的物质。
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So this isn't the most useful form that we can have, but what we'll see shortly is that from this, we can then derive further criteria for essentially any set of variables or any set of external constraints, like constant temperature or pressure or volume and so forth that we might set.
所以这不是我们所能得到的最有用的形式，但是我们会很快看到，我们能够进一步推导出包含任意变量,或者任意约束的自发过程判断标准，比如说恒定的温度，压强,体积或者其他我们能够给出的约束。
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Let's say we start from some V1 and p1 here, so high pressure, small volume and we end up with a high volume low pressure, under constant temperature condition.
例如我们要从压强比较高，体积比较小V1，p1出发,到达低压强，大体积的末态，过程中温度不变。
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So that's going to results in an expansion where the new volume new temperature new pressure and an external pressure, p2 which is p2 which is a smaller pressure.
这样经过膨胀,到达了,状态为V2，T2，p2的末态，外界压强也降低到。
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So we're going to start with a mole of gas, V at some pressure, some volume, T temperature and some mole so V, doing it per mole, and we're going to do two paths here.
假设有1摩尔气体，具有一点的压强p，体积，温度，我们将让它，经过两条不同的路径。
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du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.
偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。
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