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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
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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。
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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。
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"His name is John Barovetto, B-a-r-o-v-e-t-t-o.
VOA: standard.2010.05.31
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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
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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
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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。
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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。
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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
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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。
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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。
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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。
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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。
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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。
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/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。
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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。
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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。
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In other words, u is a function of T and V.
话句话说，u是T和V的函数。
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Path number 1 I'm going straight up in the V-T diagram.
路径1在T-V图上,竖直向上。
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So we're going to start with a mole of gas, V at some pressure, some volume, T temperature and some mole so V, doing it per mole, and we're going to do two paths here.
假设有1摩尔气体，具有一点的压强p，体积，温度，我们将让它，经过两条不同的路径。
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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。
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V Let's control T and V.
我们控制温度T和体积。
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T It's just equal to V over T.
把气体状态方程代入得到V除以。
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Only V, p and T appear.
只有体积V，压强p和温度T出现。
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I think you can tell by analogy with what I did in one dimension that the position of that object at any time t is going to be the initial position plus velocity times t plus one half a t square.
你们可以类比一下我在一维情况下的结论,这个物体在任意时刻 t 的位移,等于初始位移,加上 v ? t + 1/2 ? a ? t^2
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