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And it's always going to come down to calculating the appropriate free energy, and how it changes in the process.
这总是涉及到计算,适当的自由能，以及这些自由能在过程中如何变化。
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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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But we see if we have a free electron, as we do in this dotted line here, that's going to be a higher energy that's less stable.
但是我们看到如果,我们有一个自由电子，就像虚线所示那样，那将会是一个较高的,不够稳定的能量。
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And so the energy is zero because the electron is no longer bound. It is free.
所以这个系统能量为0，因为,电子不再受束缚了，它自由了。
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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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The Gibbs free energy. Notice, we could also write, let's rewrite that.
吉布斯自由能，注意，我们还可以这样写，重写一下。
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And so that led us to the definitions of other energy quantities, the Helmholtz and Gibbs free energy.
这就要求我们定义,其他的和能量相似的物理量，亥姆赫兹和吉布斯自由能。
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So I can in a very straightforward way say, OK, well, here is my Helmholtz free energy.
所以我可以很直接的说，这就是我的亥姆赫兹自由能。
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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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What that's going to allow us to do is, if we say, OK I have a mixture of stuff, how does the free energy change?
我们能够说的是，如果我们有一份混合物，自由能怎么变化？
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Where the Gibbs free energy, TS u plus pV minus TS is H minus TS.
吉布斯自由能等于，内能u加上pV减去TS，也是自由焓H减去。
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And that's why the Gibbs free energy is just so enormously important.
吉布斯自由能G在平衡态取得最小值,吉布斯自由能是最重要的。
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It is a free electron so there is no potential energy to be accounted for.
对于自由电子,因此没有什么势能。
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So, if we want to go from that stable state to that less stable state, we need to put in a certain amount of energy to our system, that difference between the free electron and the electron bound to the metal.
所以，如果我们想使电子,从稳态到达不够稳定的状态，我们需要引入一定数量的,能量到系统中，即自由电子和束缚于金属的,电子的能量差。
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It's the state that has the lowest Gibbs free energy.
它具有最小的吉布斯自由能。
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In some sense, that's one reason to associate this as a kind of energy, H just like mechanical energy u or enthalpy H, it's the minimum free energy state that is the equilibrium state under the relevant conditions.
在某种意义下，这是我们把这些物理量称为能量的原因，就像机械能U和自由焓，具有最小自由能的状态在特定的条件下,就是平衡态。
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So, if, for example, we were looking at a hydrogen atom in the case where we have the n equals 1 state, so the electron is in that ground state, the ionization energy, it makes sense, is going to be the difference between the ground state and the energy it takes to be a free electron.
电离氢原子所需要的能量,如果我们看n等于1的情况,电子在基态，那电离能，很合理的就是基态,和自由电子态的能量差。
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