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。
The free energy increases monotonically with increasing radius.
自由能随半径的增大而单调地增加。
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 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。
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。
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。
This paper presents the steps, program chart and computing example of the minimum free energy method.
本文给出了最小自由能法的计算步骤、程序流程及言例。
It will be the release of information of the free energy, of the secret space program and other things.
自由能源的知识、秘密太空计划和其它真相都会公诸于世。
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。
Those people who talk about our Technology and "Free Energy", these are the people who have some different agenda.
这些讨论新能源和凯史科技的人有他们不同的议程。
The resulting pollution-free energy will be enough to power the tower and several buildings in the surrounding area.
由此产生的无污染能源将足以为整座塔及周边若干建筑进行供电。
There is no further need to pollute planet Earth once free energy, zero point energy devices are in the public domain.
根本就没有必要再去污染行星地球，只要自由能源出现，零点能源设备出现在大众领域。
Especially when you're talking about something like a chemical potential, which is really nothing but the Gibbs free energy.
尤其是当你谈论诸如,化学势之类的东西的时候，实际上这就是吉布斯自由能。
We learned that the pressure dependence of the Gibbs free energy gives you the pressure dependence for the chemical potential.
我们还知道吉布斯自由能，对压强的依赖关系决定了，化学势对压强的依赖关系。
This is not a "Free Energy". If nuclear energy is free, if oil industry is free, then the plasma technology is free, too.
如果核能是免费的，石油工业是免费的，那么等离子技术也是免费的。
With respect to pressure, when we know that the variables that we use for Gibbs free energy are pressure and temperature. Right?
对压强求导，你知道吉布斯自由能，的变量是压强和温度？
So of course, the free energy in either case is just the sum of the number of moles of each times the chemical potential of each.
那么当然，任一种情况的自由能，就是各组分的分子数，乘以化学势再加和。
Question: Can you tell us about the "free energy" that has been around since the 30's, or is it wind, solar and water energy?
问：问：你说30年代就存在了的“自由能源”是指什么？是风能、太阳能、水能吗？
Previous experiments and simulations, however, indicated that the free energy of hydration did not match this predicted linear trend.
然而，过去的研究和模拟表明，烷烃的水化自由能并不符合预计的线性变化趋势。
Previous experiments and simulations, however, indicated that the free energy of hydration did not match this predicted linear trend.
然而，过去的研究和模拟表明，烷烃的水化自由能并不符合预计的线性变化趋势。
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