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The only function it is -- it doesn't care where the gas is. It only cares where the temperature is.
是温度的函数,它只是温度的函数,不管是什么气体。
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In other words, now I know how to tell how the Helmholtz free energy changes as a function of temperature.
换句话说，我现在知道如何写出亥姆赫兹,自由能作为温度的函数。
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are all functions of state and parameters that we can control like temperature and pressure.
公式里面的全部都是态函数,我们控制态函数的参数比如温度或者压强。
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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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You need a functional form that connects the value at one state of matter, the freezing point of water to another phase change, the boiling point of water.
你需要一个函数形式来,连接物质某个态对应的温度值，如水的冰点，和另一个相变,如水的沸点。
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There's a volume, there's a temperature, than the pressure here. There's other volume, temperature and pressure here, corresponding to this system here.
温度等状态函数有本质区别，这个状态有一组，确定的体积，温度与压强。
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So that you could see that for the ideal gas, u would not be a function of volume, but only of temperature.
所以我们可以看到对理想气体，内能不依赖于体积，而仅仅是温度的函数。
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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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So for an ideal gas, we saw that u was only a function of temperature.
对于理想气体，我们知道内能只是温度的函数。
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But it's allowed to say the internal energy is a function of temperature and volume.
但是我们也可以说内能,是温度和体积的函数。
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Similarly for G as a function of temperature and pressure, I can go through the same procedure.
同样的G作为,温度和压强的函数，我可以采用相同的步骤。
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Pressure has dropped out of the picture completely here. So there is no p dependence here.
理想气体的H只是温度的函数,这对于真实气体来说是。
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That u is a function of temperature only.
内能只是温度的函数。
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It's the function of temperature, as B.
它是温度的函数。
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In general, temperature and volume or pressure.
一般来说写成了温度，体积和压强的函数。
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Cv So, for Cp and Cv, these are often quantities that are measured as a function of temperature, and one could, in fact, calculate this integral.
一般Cp和,都是温度的函数，因此实际上，我们可以将这个积分计算出来。
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Therefore, from experiments, u is only a function of temperature for an ideal gas, H and therefore from these experiments, 0 we come out with delta H dH/dp is equal to zero.
因此，从实验可以得出,对于理想气体u只是温度的态函数，因此从这些实验中我们得到Δ,偏H偏p等于。
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Now, before, of course, in the first part of the class u we started out looking at u H and then looking at H not as functions of S and V or S and p, but as functions of temperature, mostly.
现在，在本课的前一部分,我们首先讨论了,然后讨论了,这两个量并未写成S和V或者S和p的函数，而是写成了温度的函数。
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