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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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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 in particular let's look at, for example, du/dV du/dV at constant temperature.
更特殊一点考察，恒定温度下的。
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It's a state function, so we're at constant temperature and pressure, and now we want to consider some chemical change or a phase transition or you name it.
这就是态函数，我们处于恒定的温度和压强之下，然后考虑某些化学变化或者相变,或者你想考虑的东西。
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And so, again, we see a temperature increase, and we know the work, and the temperature increase, it's a constant pressure thing.
好，我们看到温度升高了，然后我们有做功量和温度的升高量，这是一个恒定压力下的值。
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dS/dV And that, now, we know must equal dS/dV, with a positive sign. At constant temperature.
我们知道这个等于恒定温度下的，符号为正。
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Then we can take the derivative of that quantity, when we vary the temperature, holding the volume constant.
即恒定体积，改变温度，这里恒定温度下。
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OK, so we have constant temperature, because it's isothermal.
好，现在系统有恒定的温度，因为它是绝热的。
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V So this nR over V. And then, using the relation again, T we can just write this as p over T.
恒定温度下的dp/dT等于nR除以，再次利用状态方程，可以把它写成p除以。
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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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p Well, it's not just p dS/dV because there's some dS/dV at constant T.
它不是简单的,因为式子中还包含，恒定温度下的。
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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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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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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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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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So then, just like we saw, analogous to what saw just before, dS/dp it's T dS/dp at constant T.
就像我们看到的,就像我们刚才看到的一样，结果是T乘以恒定温度下的。
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dS/dV There's some variation, dS/dV, at constant temperature.
这里有一点变化，即恒定温度下的。
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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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Experimentally, though, that's not such an easy situation to arrange.
但是保持熵恒定在实验上很难实现，当然保持温度。
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dG/dp And this is dG/dp at constant temperature.
这是恒定温度下的。
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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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In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
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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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What is dH/dT as a function, keeping pressure constant, what is dH/dp, keeping temperature constant?
恒定时偏H偏T是什么,温度恒定时的偏H偏p又是什么呢？,好的，让我们解决第一个问题？
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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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dA/dT dS/dV So this is negative dS/dV.
是负S，It’s，negative，S。,这个二阶偏导数是负的恒定温度下的。
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