Equation of State for Solids (Dense Fluids?)

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SUMMARY

The discussion centers on a proposed equation of state for solids, expressed as V[P,T] = Vi - (C1)P + (C2)T, with an internal energy equation U[P,T] = (C3)T - (C2)PT. Constants C1, C2, and C3 are critical to the formulation. The author questions the simplicity of the model, suggesting that non-linear terms may be necessary for a more accurate representation. The equations are deemed valid for small changes in pressure and temperature, reflecting the expected behavior of solids under these conditions.

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JackPunchedJi
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Stumbled across an old journal a few weeks ago that suggested the equation of state for a solid could be written:

V[P,T] = Vi - (C1)P + (C2)T

with an internal energy:

U[P,T] = (C3)T - (C2)PT

C1, C2, C3 being constants of course.

Does this make logical sense? It seems awfully simplified. I would assume there would be some non-linear terms in the equation of state itself (such as a T^2 or PT). Can't seem to find the paper either, but would love to look over it again if anyone is aware of what I am ranting about.
 
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It looks like a linearized (Taylor expansion) equation of state.
The solid has a nominal volume Vi and I know that if increase the pressure the volume should reduce (thus the sign) but, if I increase the temperature the solid expands.
Very simple indeed, it should be valid for small changes of p and T.
 
Does the relation to evaluate the internal energy of this equation of state seem valid? It's been a while since I've taken a thermo course.
 

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