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And you already saw last time there was this relationship between the temperature and volume changes along an adiabatic path.
是条绝热路径，而上次你已经看到,沿着绝热路径温度和体积,的变化有这个关系。
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Now, the coefficient that relates the amount of heat in to the temperature change is obviously going to be different for these two cases.
在这两个例子中,很显然联系热量和温度变化的系数,是不一样的。
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Some of the challenges that you see here I mentioned before, so there are problems with drought, with pests, with temperature changes and the like.
我之前提到的,你们所见的这些挑战,如干旱问题,虫害问题以及温度变化之类的
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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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We looked at pressure change before, actually, in discussing the third law, the fact that the entropy goes to zero as the absolute temperature goes to zero for a pure,perfect crystal.
在讨论热力学第三定律的时候，我们讨论过压强变化,即对于纯净的完美晶体,随着温度下降到绝对零度熵也变成零。
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Now, I know how to relate the heat flow to temperature change, through the heat capacity.
现在我知道怎样把能量的流动,和温度的变化联系起来，通过热容。
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So again with the Gibbs free energy, now I see how to determine, if I change the pressure, if I change the temperature by some modest amount, how much is the Gibbs free energy going to change?
再一次通过吉布斯自由能，我知道当我，适当的改变压强和，温度的时候，吉布斯自由能如何变化？
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Heat capacity relates the amount of heat that you add to the system to the change in temperature, and this is the relationship.
热容联系起给系统提供的,热量和温度的变化，关系式是这样的：
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Now to make that happen, it's not adiabatic, right. If I wanted to do that, I'd need a heating element or something to cool, so I could make that temperature change happen, right.
要实现这点，它就不会是绝热的，对吧，如果我想做到这点,我需要一个加热元件或什么制冷的东西,这样我才能让温度变化。
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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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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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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 that tells us what to do to know the entropy as the temperature changes.
这告诉我们当温度变化时,如何得到熵的数值。
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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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All you care about is what was the temperature change?
所有需要关心的就是温度的变化？
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This is real, unlike the Joule coefficient which is very small so that most gases have tiny Joule coefficients. So if you do a Joule experiment, you hardly measure a temperature change. With real gases, here you do actually measure it. You can feel it with your finger on your bicycle tire.
系数那样小以至于,大多数气体的焦耳系数,都很小，所以如果你做焦耳实验,很难测量出温度的变化,对于真实气体，你可以测量它，你能通过手指按在,自行车轮胎上来感觉到它。
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It's reversible. It's a temperature change.
是可逆的，温度是变化的。
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We discovered that the quantity dA, under conditions of constant volume and temperature, dA TS And A is u minus TS.
我们发现在恒定的体积和温度下，亥姆赫兹自由能的变化，小于零，is，less，than，zero。,亥姆赫兹自由能A等于内能u减去。
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It's tabulated in books, and this we can measure p in the experiment. Delta p here is the change in pressure from the left side to the right side, and we can put a thermometer, measure the temperature before the experiment and measure the temperature after the experiment.
这列在书上，这个量我们在,实验中也可以测量，在这里Δ,是从左边到右边的压强变化，我们可以放一个温度计，去测量实验前的温度,再去测量试验后的温度。
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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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Over here, we have dq=Cp dT, the heat, the proportionality between heat - and temperature rise is given by this, the constant pressure heat capacity.
这里我有dq=CpdT，这是热量，这是联系热量,和温度变化的系数，恒压热容。
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T That dS is greater than dq over T.
对吗，熵的变化dS大于热量dq除以温度。
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V2 And there's going to be some volume V2 and some volume V1, but are not necessarily the same. Especially since the pressures are different. we don't know yet about temperature so I don't know what to say about these volumes because I don't know what the temperatures' are going to do.
这里的体积会变成2,这里的容积是V1，它们不必相等,尤其是当压力不相等的时候,我们还不知道温度,所以我不能说这里的容积,是多少因为我不知道,温度会怎样变化。
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