This curve here with the square shows you how many millions of vaccine doses were distributed across the U.S.

这个带方形的曲线图显示了,在美国数以百万计的,疫苗是如何使用的

耶鲁公开课 - 生物医学工程探索课程节选

So I'm going to write that immediately here, u=0 because I know the answer to that path here.

等温过程，我们可以得到，Δ

麻省理工公开课 - 热力学与动力学课程节选

Here is the price-earnings ratio for the U.S. stock market from 1881 to the present-- this is also on that spreadsheet that you have on the website.

这是美国股票市场的市盈率,从1881年至今,这份数据也在网站上的电子数据表上

耶鲁公开课 - 金融市场课程节选

This is--I'm showing here U.S. data, but Siegel also argues in the latest edition that the equity premium is also high for advanced countries over the whole world.

这就是。。。我在这展示的是美国的数据，但是西格尔在他最新出版的书中讨论道,在世界范围内许多发达国家的,股票溢价同样很高。

耶鲁公开课 - 金融市场课程节选

So delta u is zero here.

这样，对理想气体。

麻省理工公开课 - 热力学与动力学课程节选

OK, delta H is delta of u plus pV. By definition that's how we define enthalpy up here.

好，ΔH=Δ,根据定义，这就是我们。

麻省理工公开课 - 热力学与动力学课程节选

So here are results for pathway A, right, for delta u zero delta H zero. I didn't actually explicitly write it or did I?

这是路径A的结果，△U是零,△H是零，我没有明确地写出来,是吧？让我们把它再写一遍？

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

du/dV under constant temperature was equal to zero for an ideal gas. And by analogy, we expect the same thing to be true here, because enthalpy and energy have all this analogy going on here. So let's look at an ideal gas.

偏U偏V在恒温下等于零,可以类比，我们希望在这里也一样，因为焓和能量有很强的类比性，让我们看看理想气体,【理想气体】

麻省理工公开课 - 热力学与动力学课程节选