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Then we can take the derivative of that quantity, when we vary the temperature, holding the volume constant.
即恒定体积，改变温度，这里恒定温度下。
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So the first path then, the first path, 1 constant volume constant V, so I'm going to, again, let's just worry about energy.
首先，是路径，等压过程。
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I take V1 to V2 first, keeping the pressure constant at p1, then I take p1 to p2 keeping the volume constant V2 at V2. Let's call this path 1.
容易计算的路径，第一条路径，是首先保持压强不变,体积从V1压缩到。
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That is, most processes that we're concerned with, they'll happen with something held constant like pressure or temperature or maybe volume.
这句话是说我们所关注的大部分过程，发生的时候都是保持某个量为常数,比如压强，温度或者体积。
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On the other hand, temperature, volume and pressure are variables that are much easier in the lab to keep constant.
另一方面，温度，体积和压强,在实验室中比较容易保持恒定。
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We're not going to have the constant pressure heat capacity, we're going to have the constant volume heat capacity, right.
这里出现的,不是等压热容,而是等体热容。
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It's related to the heat capacity, the constant volume of heat capacity and something you could measure.
它联系了热能，恒容热容和一些,我们能够测量的物理量。
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And the equation of state, pressure versus volume at constant temperature, is going to have some form, let's just draw it in there like that.
系统的态函数，恒温下压强比体积，变化曲线，就像这样。
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Because we did work at constant pressure, and so it's just volume difference times pressure.
因为是在恒压下做功，所以功就等于体积变化乘以压力。
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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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Now, you know with constant volume, H now it's not going to be delta H that's U straightforward to measure, it's going to be dealt u, all right.
好，现在你们知道在体积恒定的条件下，我们得到的不是Δ,我们直接测量到的是Δ,好，但这基本上也是一样的。
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So now we have a constant volume reversible temperature change.
所以现在我们有一个,等体，可逆的温度变化。
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When I flail my arms around I generate work and heat. This is not a constant volume process.
这不是一个恒容过程,但如果我是一个系统，当我做这些的时候。
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You just change volume to pressure and basically you're looking at enthalpy under a constant -- anything that's done at a constant volume path with energy, there's the same thing happening under constant pressure path for enthalpy.
可以看到这就是把体积换成了压强,一般我们都是在一种恒定状态下,考虑焓的，任何在恒容条件下,能伴随能量变化的东西，也在恒压条件下伴随焓同样地变化,所以你可以经常。
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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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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。
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It's not constant pressure, because we have a delta p going on. It's not constant volume either.
也不是恒容，这个限制,是这个实验的限制。
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So what we've discovered from this relationship dq that du at constant volume is equal to dq v.
从这个关系式里我们发现,恒体积时的du等于恒体积时的。
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We know how the volume and temperature vary with respect to each other at constant pressure.
知道在恒定压强下,体积如何随着温度变化。
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You know how pressure changes with temperature at constant volume if you know the equation of state.
如果你知道状态方程,知道在体积恒定的时压强如何随着温度变化。
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So this is still adiabatic. It's insulated, but now it's constant volume, OK.
这仍然是绝热的，是隔热的，但现在它的体积是恒定的。
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It's now, all we have to do is say we're going to have heat at constant volume.
我们需要做的就是,计算恒定体积下的热量。
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dw=0 Well for constant volume, dw is equal to zero.
约束是恒定体积，此时。
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And it's still adiabatic, but now it's constant volume. And it's also reversal right.
它仍然是绝热的，但现在是,在等体条件下，它也是可逆的。
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How do I keep p1 constant while I'm lowering the volume?
怎么保持压强不变,而减小体积？
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Yes, and if we have gases involved, it's pretty similar, but now what will have is something like this. We'll have a reaction vessel that's sealed, it's constant volume.
如果涉及了气体，情况也很相似，只是现在的装置是这样的,我们有一个密封的反应容器,它的体积是恒定的。
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So I need, well the pressure is constant, but there's a change in volume.
压强不变，体积变化。
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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If I'm working under conditions of constant temperature and volume, that's very useful.
如果在恒定的温度和体积下,进行一个过程，这是非常方便的。
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OK, for constant volume, this is zero.
对于恒定体积过程，第二项等于零。
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