The ideal gas constant doesn't change, temperature doesn't change, and so v we just have minus nRT integral V1, V2, dV over V.

理想气体常数不变，温度也不变，因此,是负的nRT，积分从v1到v2，dv除以。

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 for an ideal gas then, dH/dp under 0 constant temperature, that has to be equal to zero.

所以对于理想气体,偏H偏p在恒温下，等于。

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。

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Now, for an ideal gas, du/dV under =0 constant temperature is equal to zero.

对于理想气体，温度一定,时偏U偏V等于零。

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

If you have a real gas and you write du is Cv dT and your path is not a constant volume path, then you are making a mistake. But for an ideal gas, you can always write this. And this turns out to be very useful to remember.

对于真实气体，如果其变化过程,不是恒容的，du=Cv*dT就不成立，但对于理想气体,这条规则永远成立,这一点非常有用，请记住。

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】

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