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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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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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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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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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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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SdT This has minus T dS minus S dT, but the dT part is zero because we're at constant temperature.
这一项包含负的Tds和，但是dT的部分等于零,因为温度为常数。
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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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dG/dp And this is dG/dp at constant temperature.
这是恒定温度下的。
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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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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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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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The purpose here is to look at a series of processes in which temperature is held constant, and we're going to calculate how much work we get from allowing a gas to expand under various conditions.
目的是让大家了解一下,几个保持温度不变的过程，然后我们将计算,气体在不同膨胀过程中,的对外做功。
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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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