导出了当单位床层体积中气泡数目对气速的二阶导数为零时发生流型转变，该模型的计算机结果与实验数据吻合良好。

When the second derivative of the bubble number in unit bed volume with respect to gas velocity equals zero, the flow regime transition occurs. The model fits fairly well with the experimental data.

youdao

我现在所要做的一切就是，考察自由能对，温度，体积和压强的偏导数。

So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.

youdao

二阶导数给出熵，随着变量变化的情况，这些变量包括压强或者体积。

Then the second derivative gives the change in entropy with respect to the variable that we're differentiating, with respect to which is either pressure or volume.

youdao

So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.

我现在所要做的一切就是,考察自由能对,温度，体积和压强的偏导数。

麻省理工公开课 - 热力学与动力学课程节选

Can determine how entropy is going to behave as the volume changes.

这些偏导数,你就可以知道当体积变化时熵如何变化。

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