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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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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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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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You just change volume to pressure and basically you're looking at enthalpy under a constant -- anything that's done at a constant volume path with energy, there's the same thing happening under constant pressure path for enthalpy.
可以看到这就是把体积换成了压强,一般我们都是在一种恒定状态下,考虑焓的，任何在恒容条件下,能伴随能量变化的东西，也在恒压条件下伴随焓同样地变化,所以你可以经常。
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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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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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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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I mean maybe up the street we whisper, but here we know it. And, so here is a different kind of system where we have a constant external pressure.
或许在街上你们低声细语，但在这里不应该这样，这是另一个系统,我们有一个恒定的外压强。
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dV dT Is equal to minus dV/dT at constant pressure.
它等于，负的恒定压强下的。
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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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dG/dT That is, this is, dG/dT at constant pressure.
这就是恒定压强下的。
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If I keep the pressure constant.
当我保持压强恒定。
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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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p So dV/dT at constant pressure is just nR over p.
所以恒定压强下dV/dT等于nR除以。
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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T So we know that T dS/dT at constant volume is Cv over T, T and dS/dT at constant pressure is Cp, over T.
在恒定压强下定压比热容Cp乘以dT除以,所以在恒定体积下dS/dT等于Cv除以，在恒定压强下dS/dT等于Cp除以。
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Let's take a system. Under constant pressure T1 V1, going to a second -- this is the system, so let me write the system here.
我们建立一个系统1,在恒定的压强T1，V1，下，变成了另一个系统，-这个初始的系统让我把它写在这。
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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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du But here you've got pressure constant. du, T this is du, not H here. du/dT is only equal Cv to Cv when the volume is constant, not when the pressure is constant.
这里是压强横笛，du，这是，不是H，偏U偏,只在体积恒定时等于，而不是压强恒定时。
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