Equation of State for Solids (Dense Fluids?)

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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 relation U[P,T] = (C3)T - (C2)PT. The simplicity of this formulation raises questions about its validity, particularly regarding the absence of non-linear terms like T^2 or PT. It is noted that while the equation may hold for small changes in pressure and temperature, it appears to be a linearized version, potentially limiting its applicability. The relationship between pressure, temperature, and volume is acknowledged, with the expectation that increased pressure reduces volume while increased temperature causes expansion. Overall, the discussion highlights the need for further exploration of the equation's assumptions and potential limitations.
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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