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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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To ask questions like how much heat is released in a chemical reaction that takes place at constant temperature.
当我们想要知道,当一个化学反应在恒定的温度下发生时,会放出多少热量时。
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Avogadro was a professor of chemistry at the University of Turin who did a lot of work on gas laws, understanding the number of gas particles in a given volume at a given temperature.
阿伏加德罗是一个化学教授,在都灵大学,他做了很多关于气体定律的研究，了解气体微粒,在特定的容量和温度下的数目。
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And that will end up winning out at basically any realistic temperature where the stuff really is a gas.
在体系仍然处于气体状态的温度下,熵战胜了能量。
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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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Whereas under these conditions, these quantities, if you look at free energy change, for example at constant temperature and pressure, H you can still calculate H.
但是，在这些条件下，这些物理量，如果我们考察自由能的变化,例如在恒定的温度和压强下，我们仍然可以计算。
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And you can find these compressibility factors in tables. If you want to know the compressibility factors for water, for steam, at a certain pressure and temperature, you go to a table and you find it.
各种气体的压缩系数,想知道水或者水蒸气,在某个温度和压强下的，压缩系数，查表就行了，这是实际气体状态方程的。
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That is, it's easy to write down straight away that dG with respect to temperature at constant pressure S is minus S.
这就是说，可以很简单的写出dG在,恒定压强下对温度的偏导数,是负。
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A It tells me that the partial of A with respect to T at constant V is minus S. Right?
他告诉我们,在恒定体积下对温度的微分等于负S，对吗？
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Because so much of what we do in chemistry does take place with constant temperature and pressure.
因为化学中我们所做的很多东西,都是在恒定的温度和压强下进行的。
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There's our condition for equilibrium at constant temperature and pressure.
这就是我们在,恒定温度和压强下的平衡条件。
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State one goes to state two. Let's have constant T.
在恒定的温度下。
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And where does that happen, At what temperature and pressure and so forth.
在什么温度，和压强下。
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If I'm working under conditions of constant temperature and volume, that's very useful.
如果在恒定的温度和体积下,进行一个过程，这是非常方便的。
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You're running, you're shaking a beaker up here at room temperature.
你跑步，震动烧杯，这都是在恒定温度和压强的情况下的过程。
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But now, so this is where the refrigeration comes in. So if you take a gas, and you're below the inversion temperature and you make it go through this irreversible process, the gas comes out colder from that side than that side.
这就是冰箱的原理,如果在低于转变温度,的情况下我们将气体经过,这个不可逆过程,气体出来的温度将比这边低。
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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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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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pV Also A plus pV and G is minimized at equilibrium with constant temperature and pressure.
同时等于亥姆赫兹自由能A加上,同时在恒定的温度和压强下。
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p dA/dV, at constant T, must be negative p.
在恒定温度下，dA/dV等于。
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The dA/dV is calculated at constant temperature.
就像这样，dA/dV是在恒定温度下的偏导数。
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Or I could have a non-adiabatic, I could take the same temperature change, by taking a flame, or a heat source and heating up my substance. So, clearly q is going to depend on the path.
也能改变温度，绝热指的是没有热传递，在非绝热条件下，也同样可以升温,比如用火或者热源加热，这样，q也应当与路径有关。
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So in this experiment here, delta p is less than zero. You need to have this whole thing greater than zero. So delta T is less than zero as well. So if you're below the inversion temperature and you do the Joule-Thomson experiment, you're going to end up with something that's colder on this side than that side.
所以在这个实验中，Δp小于零,这全部都大于零,因此ΔT也小于零,所以如果在低于转变,温度的情况下做焦耳-汤姆孙实验,最后的结果是,这边的温度比这边低。
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