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。
But, of course, it's going to come from the fact that these second derivatives are also equal.
但是,结果同样是依赖于,二阶混合偏导数相等。
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。
G We can take the derivative of G with respect to how much material there is.
我们可以取,对物质总量的偏导数。
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。
These things have to be equal to each other.
这两个偏导数是相等的。
Because these mixed second derivatives are the same thing.
因为这两个混合二阶偏导数,是相等的。
Now let's take it in the other order.
我们用另一种顺序求二阶偏导数。
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。
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。
So d/dT of dA/dV, just like this.
即对dA/dV求对温度T的偏导数。
dA/dT dS/dV So this is negative dS/dV.
是负S,It’s,negative,S。,这个二阶偏导数是负的恒定温度下的。
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。
With respect to n, the number of moles.
对n的偏导数,这里的n是摩尔数。
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