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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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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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Now, we can immediately see what du/dV at constant entropy is.
我们能够很容易看出,恒定熵的条件下du/dV的数值。
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du/dV at constant T. And so, what is it?
求恒定温度下的du/dV，但是，这个量是什么？
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It's constant pressure. OK, so now, last time you looked at the Joule expansion to teach you how to relate derivatives like du/dV.
这是恒压的，好，上节课你们,学习了焦耳定律,以及怎样进行导数间的变换。
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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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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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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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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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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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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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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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