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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。
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It's definitely not an ideal situation. Generally don't do as well on those.
这当然不是什么理想的情况。这样的考试一般考得不怎么好。
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This needs to be stressed that this is the ideal gas case. Now regular gases, real gases fortunately as I said, don't obey this.
需要强调的是这是对理想气体而言的,普通气体，真实气体，就像我说过的,不遵循这个规律，这是非常重要的。
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We don't have the ideal world that I just described, but to some extent we do, so we want to think about diversifying in this world.
现实世界并不像我刚才说的那么理想，但在某种程度上这种现象还是存在的,所以同样也要考虑多元化的问题。
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So he couldn't find his ideal woman and he went back to Athens.
他找不到理想中的女人，于是他返回雅典。
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It's absolutely constitutive of the ideal of freedom, of our freedom; because if we don't try everything, if we don't give ourselves an opportunity to decide for ourselves, then, of course, someone will invariably be making those decisions for us.
它也构成了自由的理念，我们的自由;,因为如果我们不是尝试过所有东西，如果我们不给自己做决定的机会，当然，总是有人会帮我们做决定。
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PROFESSOR BAWENDI: So, for an ideal gas, the isothermal is the easy one because the energy doesn't change.
对理想气体，等温过程最简单,因为能量不变。
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Now going from three to four right, so we have another isothermal process for an ideal gas, so I won't try to make you sing again so soon.
从第三点到第四点，这也是一个理想气体的,恒温过程，这次不用你们集体回答了。
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Therefore, if it's isothermal, the energy of the ideal gas doesn't change.
理想气体的，能量不变。
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It's true for any gas, and if I remove this limit here, r t is equal to p v bar, I'm going to call that an ideal gas.
这样的气体被称作理想气体,这就是理想气体的性质，理想气体的涵义是什么？
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I'll replace the ideal gas law for those two T's.
用理想气体定律代进去。
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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。
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If we don't have an ideal gas.
如果不是理想气体。
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