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And the idea was that gravity did work on the water and falling, and that work led to the generation of heat.
焦耳的想法是,重力对水，做了功。
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So for the reversible process, the work done is the integral under the pressure volume state function, the function of state.
对可逆过程，做的功,是压强体积态函数曲线下，的积分面积。
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Now in order to illustrate the way in which what Iser calls virtual work gets done in this regard, let me just run through a few passages quickly.
现在，为了阐释,在这点上，伊瑟尔所说的虚功是怎样做的，下面我们来快速地浏览几段话。
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It's just minus the sum of all these things, because of course these are just defined as the work done by the environment to the system.
等于负的这些东西的和，因为它们的定义是,环境对系统所做的功。
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So, it's a trivial matter, by looking at what is the weight and how far does it drop, to say OK, how much work is done by the paddle wheel.
好，让我们看看重物的质量,以及它下落的距离，就知道桨轮做了多少功。
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W1 So I have my initial state, my final state, W1 my initial state, my final state here.
再加热，做功，对系统做的总功是。
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The pressure is going to decrease along the way, but it's going to have to do more work So the majority in this case is right.
根据这个式子，做的功,因此多数派是正确的。
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Just to be clear, so it's heat extracted over the work in.
这等于取出的热量除以做的功，我重写一下这个式子。
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We're going to find other properties that do care about the history of the system like work, that you put in the system, or heat that you put in the system, or some other variables But you can't use those to define the equilibrium state.
我们还会发现其他一些,与系统的历史有关的性质,比如你对系统做的功，或者你向系统传递的热量，或其他的变量,但你不能用它们,来定义平衡态。
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In this class here, we're going to stick to one kind of work which is expansion work.
推动我的粉笔,我就对它做了功。
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All right, now suppose that I took these two paths and coupled them together.
现在假设我把这两条路径结合起来,这是路径1做的功。
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So w, the work is less for the irreversible process than the reversible process.
不可逆过程中系统对外界,做的功要比可逆过程时小。
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The energy expanded by the system is smaller for the irreversible process.
它做的,功要小些。
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So, let's calculate w1. The work for path one.
计算这两个过程中做的功。
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Wirr Minus w irreversible, this is the work which is done to the environment by the system, -Wrev minus w irreversible is always smaller than minus w reversible.
一点提示，不可逆过程中系统,对外界做的功，总是小于,之前我们。
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So if delta v is negative, in this case delta v is negative, OK, delta v is negative, pressure is a positive number, negative times negative is positive, work is greater than zero.
也就是当活塞,压缩气体的时候，做的功是正的，按照这一规定,我们需要在这里，加上一个负号，这是习惯规定。
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Delta v is going to be negative. w is going to be negative. Sorry, I got it backwards again.
这样就对外界做了功,这时候ΔV是正的。
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This is a positive number, p1 is smaller than p2.
这就是系统对外界做的功。
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So it doesn't have to do as much work.
这样它做的功也较少。
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surroundings do on the system.
被定义为外界向系统做的功。
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W2 So in this case, it's the amount of work is the area under that curve. And in this case here, the amount of work is bigger, w2 is bigger and it's the area under this curve.
这是路径2做的功,比W1要大，现在假设,我把这两条路径结合起来。
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V2 p1 times V2 minus V1. What that turns out to be, 0 this area right here. It's V1 minus V2 times p1.
第二步做的功是-pdV，积分从V2到，这部分积分出来是多少？应该是。
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V2 That's minus p1 times V2 minus V1.
做的功是-p1dV，积分从V1到。
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