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So now if I look at my V1 over V2 to the gamma minus 1, that's T2 over T1.
于是把^=中2,的两个温度。
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So what this says is the efficiency of any reversible engine T1 has to be one minus T2 over T1.
这就是说,任何可逆热机的效率都是,负T2除以。
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So, the average is found by taking two instants in time, say t1 and later t2, and you find out where it was at t2 minus where it was at t1 and divide by the time.
平均速度就是取两个时刻,比如t1和之后的t2,用t2时刻的位移,减去t1时刻的位移,再除以这段时间
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T2 So this is an isotherm at some different temperature T2, a cooler temperature, because this was an expansion.
这个绝热过程的温度是,比T1低，因为这是个膨胀过程。
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So this is just going to be T2 over T1 minus T2, that's our coefficient of performance.
这就是我们的，制冷系数。
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I'm going from T1 to T2, and I have two ways to go here. One is non-adiabatic.One is adiabatic.
从T1升温到T2有两类途径,非绝热，或者绝热。
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T1 Anyway T2 over T1 is equal to V2 over V3 to the power gamma minus one.
总之，T2除以3,等于V2除以V3的伽马减一次方。
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So we're going to start at one, T1 and this is going to be in isotherm at temperature T1, and all the paths here are going to be reversible.
我们从一开始，这是个绝热恒温过程，温度是，所有路径都是可逆的。
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T1 So this is negative T2 over T1 over negative one minus T2 over T1.
除以负1减T2除以1,我可以把这些消掉。
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One plus this, T1 but this is the same as one minus T2 over T1.
加这个，等于1减T2除以。
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So delta u is just equal to the work but we also know what happens T2 because the temperature is changing from T1 to T2.
所以Δu等于输出的功,但我们也知道它会发生,同时我们知道温度从T1变到。
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Which means that q1 over T1, that's this delta S thing that we saw before.
也就是说q1除以q2本质上是，我们之前见过的那些含Δ的量。
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T2 So we know that delta u is just Cv times T1 minus T2.
u等于Cv乘以T1减去。
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T1 So delta you is just Cv times T2 minus T1.
因此Δu等于Cv乘以T2减。
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And I compare T2 irreversible T2 They're both less than T1.
我们要比较不可逆过程的,与可逆过程的T2，to，T2，reversible。,显然它们都比T1要小。
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So it's minus R T1 dV over V, right?
那么这是-RT1，dV/V，对吧？
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p2 There is going to be an internal pressure where T1 p1 is less than p2 and there's V1 and T1 here.
内部气体压强p1小于,体积为V1，温度为。
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w This is just q plus w. There's w, RT1 ln q has to be R T1 log of V2 over V1.
而U等于q加，那是w，q应该是。
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RT So it's delta u plus RT, we can say T1 is the n temperature we've used here, delta n of the gas.
所以它应该是ΔU加,我们可以在这里用T1，气体的Δ
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Here's heat exchanged in pathway A and in pathway B heat is zero, and in pathway C, Cv here is qC it's Cv T1 minus T2.
这是qA，这是路径A上的热量交换,路径B中的热量交换是零，而在路径C中，这是qC，它是。
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/T We've got Cv integral from T1 to T2, dT over T is equal to minus R from V1 to V2 dV over V.
左边是Cv乘以，从T1到T2对dT积分。
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Let's take a system. Under constant pressure T1 V1, going to a second -- this is the system, so let me write the system here.
我们建立一个系统1,在恒定的压强T1，V1，下，变成了另一个系统，-这个初始的系统让我把它写在这。
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In B it isn't, it's Cv times T2 minus T1, right.
在B中不是，而是Cv乘以。
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V3 Namely, T2 over T1 is equal to V2 over V3.
好，就是T2除以T1等于V2除以。
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UC So we can immediately write delta u C is Cv times T1 minus T2. Delta Hc C is Cp times T1 minus T2, right?
所以我们可以直接写出△,是Cv乘以,△HC是Cp乘以，对吧？
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log We're going to have the ratio of temperatures T1 and the ratio of these logs.
和这些,最后可以得到等于T2除以。
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Fewer products and calorimeter at T1, right.
以及T1下的生成物和量热计，对吧？
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So I'll start at some initial temperature, T1.
那么我从某个初始温度T1开始。
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I've got reactants and calorimeter at T1.
我有T1下的反应物和量热计。
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Were going to make it for a mole of gas, T1 so it's R times T1, V and then we'll have dV over V.
假设是有一摩尔气体，那么就是R乘以，然后有dv除以。
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