Just imagine a (prismatic) block of material with crosssection A in a homogeneous gravitational field (so that the potential is m*g*h). It does not matter how it got there. If this blocks "moves down" by delta_h it releases the energy M*g*delta_h(1), where M is the mass of the total block, M=A*h*density(*). The question is now: is that released energy enough to melt the delta_h hight base layer of the block? It is if the energy equals H_m*A*delta_h*density(2), where H_m is the melting enthalpy of the material the block is made from and A*delta_h*density the mass of the layer that has to be melted. Equate (1) and (2) (and substitute (*) into (1)) and get: g*h=H_m. So, for h>H_m/g the lowest layer of the mountain melts away (and gets squeezed out) until the mountain reaches the critical height.
The equation (*) depends on the geometry of the mountain, it would be M=A*h*density/3 for a cone.
The height is measured in relation to the (floating) tectonic plate.
So what you're basically saying is that a big heavy mountain of material will eventually get so heavy that it's weight will generate enough energy in the form of heat to melt the base layer, thereby reducing the overall potential height?...So even with a lower density material...the melting point might be lower and could 'even things out' vs a higher density material with a higher melting point?
(love this kind of stuff...hope you're ok with my lay-mans description...I am a lay man after all) I'm assuming cfds that you are either a geologist(or related science)...or you found this on wikipedia (grin) and doing a good job of faking it.;)
Yes that is what I meant to say.
And I am a physicist, this "mountain height thing" is one of our favorite exercises in "impress people by using simple assumptions and algebra" :)
Cool...Now I know where to go with all my physics related questions (grin). I suspect that, while really interesting, this may amount to a level of detail that goes beyond the scope of s0meguy's original intent. I can say, for myself, that my world building project won't require this level of detail. In fact...I know my imaginary planet defies all kinds of 'laws of physics'. I'm using lots of divine intervention to justify things. Trying to mix a certain degree of realism with your fantasy can be a tricky balancing act.
I care a lot about realism. If something I put in my universe is something that could not physically exist, it will bug me until I have somehow justified it or removed it. But when creating a fictional universe, realism is flexible. There is no reason that another (even real) universe can't have different constants that cause elements to have different properties, and for particles to behave differently. But anyway, assuming our universe's rules:
So, the higher the melting point of the material at the core of the mountain, the higher it can become? Melting points are pretty variable between different elements, so if for some reason large deposits of rare metals accumulated there, the max height of the mountain could be a lot higher?
I wonder on what timescale mountain ranges "melt away" using those processes. Giant mountains could still be young ones.