Of course in the reversible case, you're always pushing against an external pressure, which is essentially equal to the internal pressure.
当然在可逆的情况下,外压力,总是,等于内部压力。
Because it's so important. And I should add and also under reversible work, where the external pressure is equal to the internal pressure.
而且我还要说应该在外部压强,和内部压强相等的,可逆过程中引入它。
So the force that you're pushing down on here is the external pressure times the area.
或者压缩功的概念,在活塞上施加压力。
Because what we've done is we forced p, pressure here, to be equal to the external pressure.
因为这里我们让内部的压强,等于外部的压强。
This is an example where the external pressure here is kept fixed as the volume changes, but it doesn't have to be kept fixed.
在我们举的这个例子中,外界压强不变,气体体积改变。
This piston is being brought out, so we expect 0 the work to be negative, negative. And we start o V2 ut with zero volume. We end up with a volume p2 of V2, and the external pressure is constant to p2.
所以我们可以想象功是负的,开始的时候体积是,最终的容积是,外界的压力恒为。
and when we remove one of the weights, p2 this gives an external pressure p2.
外部压强,变为。
So it's going to shoot up until the internal pressure and the external pressure are in equilibrium.
活塞将上,移直到内外,压强达到平衡。
We've changed the external pressure slowly, and again this is isothermal.
我们慢慢改变外部压强,这个过程也是绝热的。
It's reversible, that means that p external, equals p. I'm doing it very slowly so that I'm always in equilibrium between the external pressure and the internal pressure so I can go back and forth.
我都可以不损失能量,而把过程逆向进行,整个过程中的,每一步都保持平衡,现在我们来分别。
I mean maybe up the street we whisper, but here we know it. And, so here is a different kind of system where we have a constant external pressure.
或许在街上你们低声细语,但在这里不应该这样,这是另一个系统,我们有一个恒定的外压强。
I could change my external pressure through the whole process, and that's the path.
事实上外界压强,也不必固定。
First let's set the external pressure equal to zero.
首先,让外部压强为零。
to take my cylinder now, and the external pressure and the internal pressure are not going to be I'm going to start with my cylinder here, I'm going to put little pegs here so it doesn't fly up.
活塞内外的,压强不相等,我们在,放上插销,以防止活塞。
So this is the external pressure.
这是外界压强。
OK, we're going to do this reversibly, which means we're going to slowly change the external pressure very, very slightly at a time, so that at every point we're basically in equilibrium, p2/ until the pressure reaches a new smaller pressure p2.
整个过程保持可逆,外界压强,变化得很慢,每一个瞬间,都保持平衡,直到压强减小到末态值。
Remember it's the external pressure that's important. In this case, because it's a reversible process, the external pressure turns out to be always the same as the internal pressure.
是过程非常缓慢,比如我把体积,从V1压缩到V2时,我做得十分缓慢,在过程中的任何一点。
p1 So p2 is less than p1, the external pressures is less than the internal pressure.
抱歉,应该是p2小于,外界压强小于内部压强。
External pressure is p3. It's higher than p2.
外部压强为p3,比p2大。
Then you put two pistons, one on that side here and one on this side here, and the external pressure here, we're going to call that p1.
接下来我们放进两个活塞,一个在这,一个在这,这变外界的压强为p1;
So that's going to results in an expansion where the new volume new temperature new pressure and an external pressure, p2 which is p2 which is a smaller pressure.
这样经过膨胀,到达了,状态为V2,T2,p2的末态,外界压强也降低到。
So this isn't the most useful form that we can have, but what we'll see shortly is that from this, we can then derive further criteria for essentially any set of variables or any set of external constraints, like constant temperature or pressure or volume and so forth that we might set.
所以这不是我们所能得到的最有用的形式,但是我们会很快看到,我们能够进一步推导出包含任意变量,或者任意约束的自发过程判断标准,比如说恒定的温度,压强,体积或者其他我们能够给出的约束。
We're going to change the pressure above, Pext right now there's a p external, which is equal to p on the inside.
来改变外界条件,可以改变外界的压强,它将与气体压强p相等。
It's the pressure the external world is applying on this poor system here.
V是气体初态和,末态的体积之差。
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