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R They're related through the gas constant.
理想气体常数。
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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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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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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。
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How many moles of gas are there in each case, in reactants and products? If that changes, of course you know that the pressure in there is going to change at constant volume if the amount of gas in there is changing.
在反应物和生成物中，各有多少摩尔的气体？,如果它发生了变化,当然在等体条件下，如果气体的总量,发生了变化，压强也会发生变化。
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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。
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The purpose here is to look at a series of processes in which temperature is held constant, and we're going to calculate how much work we get from allowing a gas to expand under various conditions.
目的是让大家了解一下,几个保持温度不变的过程，然后我们将计算,气体在不同膨胀过程中,的对外做功。
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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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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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All right, so gamma, the gas is cooling so V2 is going to be less than it what would be if the temperature kept constant.
气体温度下降了,于是V2会比等温过程,降到相同压强时的体积要小。
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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。
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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。
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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。
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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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