# Mass to volume conversion

hubble_bubble
Is there an equation to convert mass to volume assuming a negligible gravitational effect. So say 1 micro gram occupies a particular volume.

Gold Member
The relationship between mass and volume is called the Density (look it up). Density varies from substance to substance. Gravity doesn't come into it unless you are dealing with a substance that is compressible under its own weight (say air).

hubble_bubble
The relationship between mass and volume is called the Density (look it up). Density varies from substance to substance. Gravity doesn't come into it unless you are dealing with a substance that is compressible under its own weight (say air).

OK. I am trying to understand the relationships between Planck length, Planck mass and Planck volume. The measurements are so small and have a standard uncertainty I was thinking I could scale them up somehow to say make 1 Plank volume equal to 1 cubic metre for convenience and then derive the other units from that. Don't ask me why I want to do this as it is something I am working on that is not related to current theories and would cause problems if I discussed it here.

Mentor
Scaling numbers up can easily be done by using scientific notation.

Staff Emeritus
Homework Helper
... I was thinking I could scale them up somehow to say make 1 Plank volume equal to 1 cubic metre for convenience and then derive the other units from that.
But a Planck volume is not 1 m3, it is (1 Planck length)3, or about 4 × 10-105 m3.

(If I understand your statement correctly.)

Mentor
I think the idea was to divide it by 4x10-105 to make it easier to work with.

hubble_bubble
I think the idea was to divide it by 4x10-105 to make it easier to work with.

The problem is with h-bar if I have h at 1. If I have 1/2pi for h-bar then how would this relate to G and c? The units are no longer normalised, are they?

Mentor
You aren't really explaining what you are trying to do, so I have no idea what the issue is. Perhaps you need to be working with the equations without plugging in the values?

hubble_bubble
You aren't really explaining what you are trying to do, so I have no idea what the issue is. Perhaps you need to be working with the equations without plugging in the values?

I think that is what I will have to do otherwise I am comparing apples with pears. Ultimately I want to convert mass to a volume. I need to factor in a density for a rest mass energy. I want to plot volume and mass for various elements at rest mass. Unless this has already been done. I also want to plot valency against specific gravity for elements in the periodic table. Does anyone know if this has been done somewhere.

Mentor
Yes, if you don't want to deal with ugly values, working with equations can avoid that.

And yes, you can certainly find tables of densities online. However, be aware that density is a macro phenomenon that depends on the arrangement of the atoms. There is not one single density for an element. This probably means that what you are seeking to do isn't possible.

hubble_bubble
Yes, if you don't want to deal with ugly values, working with equations can avoid that.

That's what I am thinking.

And yes, you can certainly find tables of densities online. However, be aware that density is a macro phenomenon that depends on the arrangement of the atoms. There is not one single density for an element. This probably means that what you are seeking to do isn't possible.

I know and that is going to be a real problem. I haven't worked out how to resolve it yet. I am sure there will be a way but the math will be complex. Maybe too complex.

hubble_bubble
I have been reading up on the classical electron radius. If I were to use this as a reference point and sidestep quantum mechanics (I know!) then this could give me some reference point.

hubble_bubble

hubble_bubble
Has anyone heard of the scale invariant quantum Hall impedance.

I found this.