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### Author Topic: Does the mass of a system depend on its enthalpy or its free energy?  (Read 2678 times)

#### chiralSPO

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##### Does the mass of a system depend on its enthalpy or its free energy?
« on: 29/11/2015 17:35:13 »
I was inspired by this response in another thread (I added bold for emphasis for the purposes of my question):

...At the same time, using planet-wide temperature readings from NASA and other sources, one can see that the planet is warming up, or gaining thermal energy. This is coming from the Sun, and if energy is added to a system, then since E=mc^2, there is a corresponding increase in mass. Based on present data, this is probably adding a small amount of mass to the planet each year, of the order of 200 tonnes or so.

...

At the same time, the Earth is losing heat energy from its core as radioactive elements decay. Based on estimates of how much energy exits in this way, the mass loss is trivial though at about 16 tonnes per year...

Is the energy contribution to Earth's mass derived from the enthalpy (ΔH) of the system, or does it depend on the free energy (ΔG) of the system?

Recall: ΔG = ΔH – TΔS

My intuition says it has to be ΔH = Δmc2, but if I'm wrong, I'll have to rethink some of my understanding of entropy and information.
« Last Edit: 29/11/2015 18:43:09 by chiralSPO »

#### chris

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #1 on: 29/11/2015 23:33:21 »
My understanding is that it's enthalpy.

#### lightarrow

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #2 on: 30/11/2015 08:01:32 »
I was inspired by this response in another thread (I added bold for emphasis for the purposes of my question):

...At the same time, using planet-wide temperature readings from NASA and other sources, one can see that the planet is warming up, or gaining thermal energy. This is coming from the Sun, and if energy is added to a system, then since E=mc^2, there is a corresponding increase in mass. Based on present data, this is probably adding a small amount of mass to the planet each year, of the order of 200 tonnes or so.

...

At the same time, the Earth is losing heat energy from its core as radioactive elements decay. Based on estimates of how much energy exits in this way, the mass loss is trivial though at about 16 tonnes per year...

Is the energy contribution to Earth's mass derived from the enthalpy (ΔH) of the system, or does it depend on the free energy (ΔG) of the system?

Recall: ΔG = ΔH – TΔS

My intuition says it has to be ΔH = Δmc2, but if I'm wrong, I'll have to rethink some of my understanding of entropy and information.
I would say it's neither one nor the other but that it's ΔU, variation of internal energy. If volume and pressure doesn't vary, then it corresponds to ΔH (H = U + PV → ΔH = ΔU + VΔP + PΔV); but in general it's ΔU.

--
lightarrow
« Last Edit: 30/11/2015 08:04:10 by lightarrow »

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#### acsinuk

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #3 on: 05/12/2015 12:50:46 »
But what about the solar wind bringing +ions into our atmosphere and the balancing E=mc^2 equivalent from sunlight?

#### lightarrow

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #4 on: 05/12/2015 13:21:30 »
But what about the solar wind bringing +ions into our atmosphere and the balancing E=mc^2 equivalent from sunlight?
You can use that equation only if the irradiated body stays still and this happens, in absence of other forces, if the radiation is isotropic.
This said, *if you can neglect variations of pressure and volume* of the body, the body's mass increase is simply given by ΔH, that is by the heat it absorbs (because in this case ΔU = ΔH).

In general, the body's mass increase can also be due to (mechanical or other kind) work made on it: you increase the gas' mass even if you simply compress it adiabatically.

--
lightarrow
« Last Edit: 05/12/2015 13:23:45 by lightarrow »

#### Thebox

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #5 on: 05/12/2015 13:45:18 »
My opinion is it depends on the free energy (ΔG) and  the enthalpy (ΔH) of the system and thermodynamics and entropy and the constant of force.

I.e remove force, we would weigh things at zero.

#### chiralSPO

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #6 on: 05/12/2015 14:44:16 »
My opinion is it depends on the free energy (ΔG) and  the enthalpy (ΔH) of the system and thermodynamics and entropy and the constant of force.

I.e remove force, we would weigh things at zero.

Your "opinion" adds nothing to this discussion. Of course if there is no force there is no weight (weight is a measure of force). We are discussing mass. "Thermodynamics" includes free energy, enthalpy and entropy.

#### chiralSPO

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #7 on: 05/12/2015 14:48:37 »
I would say it's neither one nor the other but that it's ΔU, variation of internal energy. If volume and pressure doesn't vary, then it corresponds to ΔH (H = U + PV → ΔH = ΔU + VΔP + PΔV); but in general it's ΔU.

--
lightarrow

Thanks, that makes sense to me.

#### ijaz

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #8 on: 05/12/2015 16:08:00 »
Mass of the system depends both on the enthalpy and the Gibbs free energy but not on the Helmholtz free energy.

#### chiralSPO

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #9 on: 05/12/2015 16:39:36 »
Mass of the system depends both on the enthalpy and the Gibbs free energy but not on the Helmholtz free energy.

That is surprising to me. Helmholtz free energy assumes constant volume (while Gibbs assumes constant pressure). Since we know that pressure is a component of the energy of a system, wouldn't it be more reasonable to use Helmholtz than Gibbs?

Also, if the free energy DOES enter into the considerations, then we have to be careful about the temperature/mass relationship--there are a number of systems for which the free energy decreases as temperature increases. Also if there is a significant contribution from entropic terms, this would further complicate the nature of black holes (if they weren't already problematic).

If we imagine a "planet-sized" sphere of liquid composed of two perfectly miscible isomeric liquids (for the sake of argument, let's say that they have identical densities and identical intermolecular interactions), let's call them A and isoA. If the two liquids are segregated into opposite hemispheres and then allowed to mix (because of my assumptions, ΔU = 0 for this process), are you predicting the total mass of the sphere would decrease?

#### ijaz

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #10 on: 05/12/2015 16:51:20 »
So I would suspect. The mass deficit being converted into energy.

#### acsinuk

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #11 on: 07/12/2015 11:39:01 »
If global warming is 1 deg then increase in energy is mass x specific heat x temperature change 1 deg.  So there is the energy increase coming from?

#### chiralSPO

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #12 on: 07/12/2015 14:22:23 »
If global warming is 1 deg then increase in energy is mass x specific heat x temperature change 1 deg.  So where is the energy increase coming from?

Mostly from the sun.

#### jeffreyH

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #13 on: 11/12/2015 15:33:15 »
I have been in hospital for about a week now as my lungs started to refuse to absorb oxygen. I have taken the opportunity to read and am working on energy vector spaces with a view to minimum entropy. I have come to some interesting conclusions. I will post anything of interest to this thread.

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##### Re: Does the mass of a system depend on its enthalpy or its free energy?
« Reply #13 on: 11/12/2015 15:33:15 »