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It's not constant pressure, because we have a delta p going on. It's not constant volume either.
也不是恒容，这个限制,是这个实验的限制。
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p So dV/dT at constant pressure is just nR over p.
所以恒定压强下dV/dT等于nR除以。
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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Adiabatic q equal to zero. It's also delta H 0 which is zero. The two didn't necessarily follow because remember, delta H is dq so p is only true for a reversible constant pressure process.
在这个过程中ΔH等于,绝热的所以q等于0，而ΔH也等于,这两个也不一定有因果关系,因为，记住，ΔH等于dq只有在恒压。
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T Remember, we're trying to get delta H, p we're trying to get dH/dT constant pressure and dH/dp constant temperature. OK, these are the two things were trying to get here.
想要得到在恒压状态下的偏H偏，和在恒温状态下的偏H偏,好的，这是两个我们，在这里想要得到的东西。
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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。
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pV=RT dT here because the pressure is constant, dV=RdT/p so dV is equal to R over p dT.
因为对1摩尔气体有，于是。
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So, the first obvious one is to take V1 to V2 first with p constant. So take this path here.
从初态到末态可以有无数种路径2,甚至像这样，我们只研究两种。
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p Well, it's not just p dS/dV because there's some dS/dV at constant T.
它不是简单的,因为式子中还包含，恒定温度下的。
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p This is going to get us dH/dp constant temperature. What is this experiment?
这帮助我们理解恒温条件下的偏H偏,那么这个实验具体是什么呢？
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Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.
一般情况下我不能这么写,因为这一项会包含pdV和，但是我们已经假定压强为常数，所以包含dp的部分等于零。
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I'm going to call it r. It's going to be the gas constant, and now I have r times t is equal to the limit, p goes to zero of p r.
如果去掉p趋于0的条件,在有限压强下都,保持RT=pV的关系。
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V All right, or p is equal to a constant divided by volume.
或者p等于常数C除以。
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I'm pressing on the gas. So I expect that to be a positive number. The pressure is constant 0 p. The V goes from V1 to zero.
我们对气体加压,所以这应该是一个正数,压强是常数，p，V从V1变成。
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And so now we have this quantity, p times v bar, and the limit of p goes to zero is equal to a constant times the temperature.
不仅仅对氢气或氮气适用，在p趋于0的极限下,它适用于任何气体。
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H We also saw that dS for constant H and p was greater than zero.
我们同样可以看到如果保持自由焓,和压强不变熵的变化dS也是大于零的。
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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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So we have dH/dT keeping pressure constant, is du/dT keeping pressure constant.
等于偏U偏T，p恒定加上，偏pv偏T，p恒定。
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OK, so now we have the other one, p dH/dp constant temperature.
好的，现在我们来研究另一个量，在恒温条件下的偏H偏。
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p dA/dV, at constant T, must be negative p.
在恒定温度下，dA/dV等于。
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P This is constant S and p.
在这里保持恒定的S和。
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U It's u, because u is to q plus w right, heat and work, but it's adiabatic. So there's no heat, exchange with the environment, and it's constant volume, so there's no p dV work, right.
什么是零？是U，因为,等于q加w，热量和功，但这是绝热的，所以系统与环境间没有热量交换；,同时它是灯体的，所以也没有pdV形式的功。
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PROFESSOR BAWENDI: p is constant here.
教授：P在这里是常数。
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