There's still not nearly enough thermal energy to have a molecules up here. So what, was the derivative of the energy with respect to the temperature?

仍然没有足够的热能使分子上升到这儿，那么相对于温度得到的，能量又如何呢？

youdao

So one way to get a small change in temperature is to take a derivative with respect to temperature.

所以得到温度微小变化的一种方法，就是对温度求导。

youdao

And what that says is that the heat capacity and of course we could take the limit of this, but we can just take the derivative of this with respect to temperature more easily.

那意味着热容，当然我们也可以做它的极限，但我们用它，对温度求导更容易些。

youdao

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。

麻省理工公开课 - 热力学与动力学课程节选

And then we can take the derivative with respect to temperature, it's just R over molar volume minus b.

这样我们求,压强对温度的偏导数，结果等于R除以摩尔体积V杠减去b的差。

麻省理工公开课 - 热力学与动力学课程节选

du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.

偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。

麻省理工公开课 - 热力学与动力学课程节选