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so I'm heating up the system in this path here, and then to connect the 2 endpoints here, a constant temperature path.
需要再用，一个等温过程，这两个状态。
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To ask questions like how much heat is released in a chemical reaction that takes place at constant temperature.
当我们想要知道,当一个化学反应在恒定的温度下发生时,会放出多少热量时。
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Well that process of control to maintain a constant environment inside our body, whether it's an environment of constant mass or constant composition, or constant temperature, is called homeostasis.
这个控制过程维持着,体内环境的恒定,不论是内环境中物质的量的稳定,或者成分的稳定,或温度的稳定,这种状态叫做内稳态
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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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Whereas under these conditions, these quantities, if you look at free energy change, for example at constant temperature and pressure, H you can still calculate H.
但是，在这些条件下，这些物理量，如果我们考察自由能的变化,例如在恒定的温度和压强下，我们仍然可以计算。
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And in particular let's look at, for example, du/dV du/dV at constant temperature.
更特殊一点考察，恒定温度下的。
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It's a state function, so we're at constant temperature and pressure, and now we want to consider some chemical change or a phase transition or you name it.
这就是态函数，我们处于恒定的温度和压强之下，然后考虑某些化学变化或者相变,或者你想考虑的东西。
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OK, so we have constant temperature, because it's isothermal.
好，现在系统有恒定的温度，因为它是绝热的。
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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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Because so much of what we do in chemistry does take place with constant temperature and pressure.
因为化学中我们所做的很多东西,都是在恒定的温度和压强下进行的。
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There's our condition for equilibrium at constant temperature and pressure.
这就是我们在,恒定温度和压强下的平衡条件。
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Path number 3 is a constant temperature path, and I already wrote the answer.
它是一个等温过程，我已经写出了答案。
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SdT This has minus T dS minus S dT, but the dT part is zero because we're at constant temperature.
这一项包含负的Tds和，但是dT的部分等于零,因为温度为常数。
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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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u=0 Constant temperature isothermal delta u is zero.
对等温过程，Δ
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dG/dp And this is dG/dp at constant temperature.
这是恒定温度下的。
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dS/dV There's some variation, dS/dV, at constant temperature.
这里有一点变化，即恒定温度下的。
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v du/dV under constant temperature. du/dT v under constant volume. You use the Joule expansion to find these quantities.
像偏u偏v，恒温下的偏u偏,恒容下的偏u偏,你们知道怎么运用焦耳定律。
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In other words, the order of taking the derivatives with respect to pressure and temperature doesn't matter And what this will show is that dS/dp dS/dp at constant temperature, here we saw how entropy varies with volume, this is going to show us how it varies with pressure.
换句话说,对温度和压强的求导顺序无关紧要,结果会表明,恒定温度下的，对应我们上面看到的，熵如何随着体积变化，这个式子告诉我们，熵如何随着压强变化。
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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。
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So we already know that. So now we can write CpdT or differential dH as Cp dT plus dH/dp, pdp constant temperature, dp.
我们已经知道了这个，所以我们现在,可以写出H的微分式：dH等于，加上恒温时的偏H偏。
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Let's say we start from some V1 and p1 here, so high pressure, small volume and we end up with a high volume low pressure, under constant temperature condition.
例如我们要从压强比较高，体积比较小V1，p1出发,到达低压强，大体积的末态，过程中温度不变。
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pV Also A plus pV and G is minimized at equilibrium with constant temperature and pressure.
同时等于亥姆赫兹自由能A加上,同时在恒定的温度和压强下。
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OK, so now we have the other one, p dH/dp constant temperature.
好的，现在我们来研究另一个量，在恒温条件下的偏H偏。
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The constraint isn't constant temperature because the temperature is going to be changing.
是在不停变化的，不是恒压,因为我们已经有Δp了。
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T Remember, we're trying to get delta H, p we're trying to get dH/dT constant pressure and dH/dp constant temperature. OK, these are the two things were trying to get here.
想要得到在恒压状态下的偏H偏，和在恒温状态下的偏H偏,好的，这是两个我们，在这里想要得到的东西。
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The dA/dV is calculated at constant temperature.
就像这样，dA/dV是在恒定温度下的偏导数。
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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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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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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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