I learn off the radio waves of 98.7 Kiss F.M.salsa/disco jams, that come from a Sony, bought even though I need a coat, even though I'm behind on my payments for the Trinitron Remote Control Color T.V.
VOA: special.2009.04.27
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?
Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.
一般情况下我不能这么写,因为这一项会包含pdV和,但是我们已经假定压强为常数,所以包含dp的部分等于零。
"His name is John Barovetto, B-a-r-o-v-e-t-t-o.
VOA: standard.2010.05.31
Therefore, mathematically at a given time t, we can trade t for v and put it into this formula.
因此,从数学角度来说,在给定的时刻 t,我们可以用 v 来表示 t,并代入这个式子
If you think of two towns down here, Brive,b-r-i-v-e,famous for its rugby, and Tulle,t-u-l-l-e,which is a capital.
如果你可以想起来这儿的两个城镇,布瑞福,b-r-i-v-e,以英式橄榄球运动而负有盛名,图勒,t-u-l-l-e,是一个省的首府
du/dT And we discover that du/dT at constant V T is equal to du/dT at constant V.
可以发现恒定体积下的,等于恒定体积下的偏u偏。
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。
It's true for any gas, and if I remove this limit here, r t is equal to p v bar, I'm going to call that an ideal gas.
这样的气体被称作理想气体,这就是理想气体的性质,理想气体的涵义是什么?
So instead of v bar, we write p v bar minus b, equal r t.
现在考虑,这些气体分子之间。
V So this nR over V. And then, using the relation again, T we can just write this as p over T.
恒定温度下的dp/dT等于nR除以,再次利用状态方程,可以把它写成p除以。
This depends on the path. It tells you right here the path is constant pressure. These don't depend on the path, right. V doesn't care how you v get there. u doesn't care how you get there.
这由变化的具体路径决定,这个小脚标表明过程是恒压的,这些量都与具体路径无关,即不管是通过什么路径使得体积变化为Δ
T p V I've got three variables, T, p and V.
一共有三个变量:
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。
If you took the derivative of this, you will get the velocity at time t, it would be: v=v0+at.
如果你对它求导,你就可以知道 t 时刻的速度,即,v=v0+at
v We don't know what it is yet. In order to change this from a p to a V, you have to use the chain rule. So let's use the chain rule.
为了把这里的p变成,我们需要利用链式法则,好,让我们使用链式法则。
The ideal gas constant doesn't change, temperature doesn't change, and so v we just have minus nRT integral V1, V2, dV over V.
理想气体常数不变,温度也不变,因此,是负的nRT,积分从v1到v2,dv除以。
We'll get an expression in which there is no t; t has been banished in favor of v.
我们现在得到了一个不含t的表达式,t被v替换掉了
You know that if you took a derivative of this, you will find v of t is v0+at.
如果你对这个式子求一次导,你将会得到v=v0+at
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。
If I don't show you any argument for v, it means v at time t and the subscript of 0 means t is 0.
如果我不对v做任何标志,那就表示t时刻的速度v,下标0表示的是t=0
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。
pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
And if I draw a diagram on a T-V diagram of T-V V1 I'm starting with some V1 here.
画出过程的,图,what,I’m,doing,here,初态是。
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。
We want a relationship in p-V space, not in T-V space. So we're going to have to do something about that. But first, it turns out that now we have this R over Cv.
我们想要p-V空间中的结果,而不是T-V空间中的,因此需要做一些变换,先来看现在的关系,它跟R/Cv有关。
/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。
And the useful outcome of all that is that p we get to see how entropy changes with one of those variables in terms of only V, T, and p, which come out of some equation of state.
这样做的重要结果是,我们得到了熵随着V,T或者,其中一个变量变化的情况,这些可以从状态方程得到。
We'll then look at the quantity, internal energy, which we define through the first law, and we think of it as a function of two variables T and V.
接下来我们考虑内能,这是由热力学第一定律定义的物理量,我们把它看作T和V的函数。
In other words, u is a function of T and V.
话句话说,u是T和V的函数。
应用推荐