So, so far we don't have a way to just write off, relate them to equation of state data.
到目前为止我们还没有办法,写出他们和状态方程之间的关系。
Let's try it with a different equation of state, that isn't quite as simple as the ideal gas case.
考虑一个不同的状态方程,这状态方程不像理想气体状态方程那么简单。
You get a set of solutions that are dependent upon -These quantum states fall out of the solution to this equation.
你得到一系列的解,这些解依赖于量子状态,和方程解不相干的解。
So let's take our one model that we keep going back to Equation of state, and just see how it works.
我们回到经常使用的理想气体模型,或者说状态方程。
I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了,因此可以用,理想气体状态方程消去。
For real gases, there's a whole bunch of equation the states that you can find in textbooks, and I'm just going to go through a few of them.
这是理想气体的状态方程,对实际气体,你可以在教科书里,找到许多描述它们的,状态方程。
And for the sake of this class, we're going to consider most gases to be ideal gases. Questions?
有问题吗?好,现在,这一方程建立了,三个状态函数之间的联系:
That is, in terms of equations of state. For any material Then we would really be able to essentially calculate anything. Anything thermodynamic.
换句话说,利用任何一种物质的状态方程,我们就能够实质上,计算所有物理量,所有热力学量。
Or, if we know the equation of state from a model, ideal gas, van der Waal's gas, whatever, u now we can determine u.
或者如果我们知道模型的状态方程,比如理想气体,范德瓦尔斯气体,无论什么,我们就可以利用状态方程得到内能。
And you can find these compressibility factors in tables. If you want to know the compressibility factors for water, for steam, at a certain pressure and temperature, you go to a table and you find it.
各种气体的压缩系数,想知道水或者水蒸气,在某个温度和压强下的,压缩系数,查表就行了,这是实际气体状态方程的。
This is going to be probably a homework at some point to do this. For now, let's take it for granted. Let's take it for granted that we know how to calculate this derivative from an equation of state like this.
这可能是将来的一个课后作业,现在,请把这当成理所当然的,理所当然地认为我们,知道怎样从一个状态,方程计算这样的微分式。
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。
You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
So from measured equation of state data, or from a model like the ideal gas or the van der Waal's gas or another equation of state you know this.
所以,从测量的到的状态方程的数据,或者从状态方程模型比如理想气体方程,范德瓦尔斯方程或者其他状态方程,我们就可以知道。
Because this is what comes directly out of an equation of state, right?
因为它,可以直接从状态方程中得到?
And again, this is something that comes from an equation of state.
我们再一次发现,这个可以从状态方程中得出。
for real gases. This is an equation of state for an ideal gases.
我们需要描述实际气体,的状态方程。
Again, if we know the equation of state, we know all this stuff.
如果我们知道状态方程,我们就可以知道所有的物理量。
So again, if you do a calculation where you're close enough to the ideal gas and you need to design your, if you have an engineer designing something that's got a bunch of gases around, this is a useful thing to use.
要研究近似理想气体的表现时,这个方程非常有用,下面再来看一个,对我们来说最有意思的,实际气体状态方程:,范德瓦尔斯方程。
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。
Remember the equation of state for Van der pV=nRT Waal's gas is not pV is equal to nRT, but p plus the attraction term.
记住范德瓦尔斯气体的状态,方程不是,而是p加上一个吸引项。
Well, then, we could just use that for our equation of state.
然后我们就可以把这些数据,作为我们的状态方程。
pV=nRT And so of course it's still pV equals nRT.
显然状态方程仍然是。
Of course, that's assuming we know the equation of state.
这意味着我们假定,我们知道其状态方程。
So again, we can measure equation of state data.
我们可以通过测量得到状态方程的数据。
One way or another, we can determine this quantity.
任何一种方法都可以给出状态方程。
We've done temperature, equations of state.
温度以及状态方程的概念。
This is called an equation of state.
这一状态方程把压强。
That's what the equation of state tells us.
这是状态方程告诉我们的。
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。
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