-
dV dT Is equal to minus dV/dT at constant pressure.
它等于，负的恒定压强下的。
-
pV=RT dT here because the pressure is constant, dV=RdT/p so dV is equal to R over p dT.
因为对1摩尔气体有，于是。
-
Now you have to know from elementary calculus that v times dv/dt is really d by dt of v square over 2.
根据初等微积分知识你们得知道,v乘以dv/dt其实就是d/2)/dt
-
P dV is equal to R dT. pV = RT for 1 mole, pdV=RdT so I just take dV here.
对等压过程，那么。
-
So if you get these two guys together you get CvdT=-pdV Cv dT is minus p dV.
把它们联系,起来。
-
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。
-
dV OK, so we've got dT here dV here.
等式的左边是dT，右边是。
-
And I know pdV what those turn out to be. It's minus S dT minus p dV.
我们知道,这最终就是负SdT减去。
-
pdV Minus S dT, that's the p dV term that's left, minus p dV.
应该是负SdT，留下的应该是pdV项负的。
-
That's where that term comes from, du/dV dV/dT.
乘以偏V偏T，p恒定，这项的来源。
-
You can take a derivative of the derivative and you can get the acceleration vector, will be d^2r over dt^2, and you can also write it as dv over dt.
你可以对导数再求一次导,你就可以得到加速度矢量,也就是 d^2 r / dt^2,你也可以写成 dv / dt
-
v du/dV under constant temperature. du/dT v under constant volume. You use the Joule expansion to find these quantities.
像偏u偏v，恒温下的偏u偏,恒容下的偏u偏,你们知道怎么运用焦耳定律。
-
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。
-
So d/dT of dA/dV, just like this.
即对dA/dV求对温度T的偏导数。
-
So I can instead of the dV here, I can insert this R over p dT.
两个p消掉了，结果。
-
RT/V this expression becomes Cv dT over T is equal to CvdT/T=-RdV/V minus R dV over V.
这样，or，RT，over，V，bar。，So，now，这个等式就,可以化成。
-
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。
-
So, from the calculus we know dv/dt=a.
由微积分我们得知dv/dt=a
-
/T We've got Cv integral from T1 to T2, dT over T is equal to minus R from V1 to V2 dV over V.
左边是Cv乘以，从T1到T2对dT积分。
-
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。
-
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。
应用推荐