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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

nRT So, dp/dT, for our ideal gas, at constant volume, remember pV is nRT.

对于理想气体状态方程pV等于，所以对理想气体。

麻省理工公开课 - 热力学与动力学课程节选

So what happens then we're going to use the ideal gas law. So it's approximately delta u plus delta nRT. That's a constant. That's a constant.

我们现在要应用理想气体物态方程,这个近似等于ΔU加上Δ,这是常数，这是常数。

麻省理工公开课 - 热力学与动力学课程节选