Who remembers? Gibbs free energy?
有谁记得？吉布斯自由能？
And that gives you the Gibbs free energy.
就得到了吉布斯自由能。
And this is the Gibbs free energy per mole.
化学势是一摩尔物质的吉布斯自由能。
A free energy market needs more than one country.
自由的能源市场需要的不止一个国家。
N The total free energy is just something times n.
整个的自由能是它乘以。
In other words, there's a free energy per molecule.
换句话说，存在每个分子的自由能。
So a pretty simple form for the Helmholtz free energy.
亥姆霍兹自由能的一个比较简单的形式。
So we go back to writing what the Gibbs free energy is.
我们回到吉布斯自由能的表达式。
The Gibbs free energy per mole of a in the liquid phase.
液相中的化学势就是，液相中每摩尔a的吉布斯自由能。
So this is the variable that goes with Gibbs free energy.
所以这就是吉布斯自由能的变量。
Per mole, which is just the Gibbs free energy of vaporization.
每摩尔·吉布斯自由能，就是汽化的吉布斯自由能。
So we need to know the free energy of each one of the species.
所以我们需要知道,就是各种物质的自由能。
Now, the chemical potential, as we saw, was the Gibbs free energy.
现在，化学势，就像我们看到的，等于吉布斯自由能。
And this is just the Gibbs free energy per mole of a in the gas phase.
气相中的化学势，就是气相中每摩尔a的吉布斯自由能。
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。
The key to this efficiency is the free energy arriving by stochastic resonance.
装置效率的关键在于随机共振所能带来的免费能量。
OK, now I have this derivative of the Gibbs free energy divided by the temperature.
现在要进行微分，对除以温度之后的吉布斯自由能。
And then we can also write this in terms of the Gibbs free energy for the reaction.
然后我们可以用反应的，吉布斯自由能把它写出来。
And I know the Gibbs free energy is just the sum of the chemical potentials, right?
我们知道吉布斯自由能，等于化学势之和，对吗？
So whatever their average free energy is, that's going to add up and give us the total.
所有不论它们的平均自由能是什么，只要把它们加起来就会得到整体的值。
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。
And it relates the temperature change in the Gibbs free energy with the enthalpy change.
这个方程把吉布斯自由能中的温度变化，和焓的变化联系起来。
So we can replace this with the change in Gibbs free energy from going from gas to liquid.
所以这一项我们可以替代它，用从气相到液相变化的吉布斯自由能。
For the Gibbs free energy it was the pressure and the temperature, the number of particles.
对吉布斯自由能是压强，温度和粒子数。
Let's see that a little more explicitly by just calculating out the free energy change of mixing.
让我们通过计算出，混合物中自由能的变化，使问题更加清楚。
An altogether different, and better, idea is to use the sea to generate green, CO2-free energy.
一个完全不同的更好的思路是，利用海洋产生绿色、无co2的能量。
He and some of his grad students wanted to use nitrous oxide as an emissions-free energy source.
他和他班上一些大学生想利用氧化氮作为无排放的动力能源。
What this is telling us is that we just have a chemical potential, of Helmholtz free energy per molecule.
这告诉我们的是，我们只有化学势，每个分子的亥姆霍兹自由能。
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？
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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