OK, but in order to relate turning these physical knob to this quantity here, which we don't have a very good feel for, we've got to have a feel for the slopes.

热量是怎么进一步改变的,但是为了把这些物量同我们，不是很理解的焓联系起来，我们对微分已经有了一定的了解。

麻省理工公开课 - 热力学与动力学课程节选

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？

麻省理工公开课 - 热力学与动力学课程节选

We can start taking derivatives of this with respect to time.

我们首先来对时间求微分

耶鲁公开课 - 基础物理课程节选

We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.

我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。

麻省理工公开课 - 热力学与动力学课程节选

Mathematically, it's done by taking the expression for R and differentiating everything in sight that can be differentiated as vector t.

从数学上看是这样的,写出 R 的表达式,并对所有可以进行矢量微分的部分,对时间 t 求微商

耶鲁公开课 - 基础物理课程节选

So, using those, now, what happens if we take the second derivative of A, the mixed derivative, partial with respect to T and the partial with respect to V.

如果我取A的二阶导数,混合导数，对T偏微分,再对V偏微分。

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