The new formulation is known as B.O.P.V., or bivalent oral polio vaccine.
VOA: special.2010.01.18
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。
We want to do that because we have too many variables here. We've already got dV p we'll get rid of p as an additional variable and replace it with V which is already in here.
我们之所以要那么做,是因为这儿有太多变量了,我们已经有了dV,我们要把,作为额外的变量消去,用已存在的V代换它。
Vdp So dH is just du plus p dV plus V dp.
所以dH等于du加上pdV再加上。
STUDENT: from the T delta V p to the delta p here?
学生:,从TΔV到这里的Δ
And our job is to find out what is the mathematical description of this path, this line in p-V's case that connects these two point.
我们的任务,就是找出,描述这条曲线的方程。
So if I take p times V to the gamma, anywhere on the path, it's going to be equal to the same relation This is going to be true for any point on the path.
结果都,将等于,初态点的,只要在这条路径上。
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。
And if you're below this temperature here, this quantity, p times v it would be negative.
压强与体积的乘积将变成负数,这可能吗?
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。
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。
T p V I've got three variables, T, p and V.
一共有三个变量:
p1 V1 OK, so in my diagram now, I have p1, V1 for my gas.
于是可以画出现在的p-V图。
As p goes to zero of p times v bar.
适用于任何气体。
Enthalpy is just u plus p V.
你想要的任何地方。
In this case, V = /P. Have two quantities and the number of moles gives you another property. You don't need to know the volume. All you need to know is the pressure and temperature and the number of moles to get the volume.
以及气体的摩尔数,就可以得到第三个量,知道压强,温度和气体的,摩尔数就可以推导出气体的体积,这称为状态方程,它建立了状态函数之间的联系。
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。
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。
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。
OK, so now we can take the result from this and put it onto a p v diagram.
好,现在我们有了结论,把它画进pv图。
Minus p, right? But in fact, if you go back to the van der Waal's equation of state b here's RT over v minus b.
再减去p,对吗,但是实际上,如果你代回范德瓦尔斯气体的状态方程,这里是RT除以摩尔体积减去。
So on the p-V diagram, then, V1 V2 p1 p2 there's a V1 here a V2 here, a p1 here a p2 here.
在p-V图上,这是。
So you know your cycle, you know, you could have a whole complicated sequence on a p v diagram of steps going back.
因此,对某一的循环过程,可以在pV图上画出,一系列很复杂的小步骤。
V All right, or p is equal to a constant divided by volume.
或者p等于常数C除以。
I'm pressing on the gas. So I expect that to be a positive number. The pressure is constant 0 p. The V goes from V1 to zero.
我们对气体加压,所以这应该是一个正数,压强是常数,p,V从V1变成。
And so now we have this quantity, p times v bar, and the limit of p goes to zero is equal to a constant times the temperature.
不仅仅对氢气或氮气适用,在p趋于0的极限下,它适用于任何气体。
So instead of p, here I'm going to put nRT over V.
于是把p写成。
So any point I pick on that path will be equal to p1, V1 to the gamma.
也就是说路径上面任取一个点,计算p,V^γ
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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