That for an ideal gas it has to be the case that there's no volume dependence of the energy.

我们可以直接推导这个结果,即证明对理想气体，内能和气体体积无关。

麻省理工公开课 - 热力学与动力学课程节选

You're allowed Cv comes out here for this adiabatic expansion, which is not a constant volume only because this is always true for an ideal gas.

绝热过程写下,这个式子是因为它对理想气体都成立，并没有用到等容过程的条件,只用了理想气体的条件。

麻省理工公开课 - 热力学与动力学课程节选

So David, the theme of David as the elected king of God, David also as the ideal king, is something else that is a theme of these books.

大卫王，他被上帝选为国王这个故事的主题，他也是一个理想化的国王，这也是这些经书的一个主题。

耶鲁公开课 - 旧约导论课程节选

To receive in the closing pages of your book one word of recognition for this aspiration, if it were possible for you to give such recognition honestly, would hearten all who believe in American ideals.

其实，在座的很多人,也认同这个，如果我们所有人都持有这种理想,并让其作为星星之火，得以燎原的话,那美国式的理想。

耶鲁公开课 - 1945年后的美国小说课程节选

Right there, and I'd like you to ook at that in your handout.

着手做这个理想的类了,我想要讲讲概念。

麻省理工公开课 - 计算机科学及编程导论课程节选

We know there is no thing called a massless rope, but most ropes have a mass, but maybe negligible compared to the two blocks you are pulling, so we'll take the idealized limit where the mass of the rope is 0.

我们都知道无质量的绳子是不存在的,是绳子就有质量,但是相比于这两个物体就可以忽略不计了,所以我们有了这个理想的条件,即绳子的质量都是 0

耶鲁公开课 - 基础物理课程节选

His idea of regime politea again the same word the same word that was used for the title of Plato's Republic is the centerpiece of Aristotle's politics literally.

他的政体概念，Politea，是同义字,且这个字还用于,柏拉图的《理想国》，而那可说就是,亚里士多德政治理念的中心思想。

耶鲁公开课 - 政治哲学导论课程节选

In other words, we're taking advantage of the fact that we now know that quantity. In the case of the ideal gas we just have a simple model for it.

换句话说，我们可以利用我们已经,了解这个物理量的这个优势,对理想气体我们有一个简单的模型。

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

For the ideal gas it's this.

对理想气体就是这个。

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