# Equation of State for Solids (Dense Fluids?)

• JackPunchedJi
In summary, the conversation discusses an old journal that proposes a simplified equation of state for a solid, with constants C1, C2, and C3. The equation suggests that increasing pressure decreases volume, while increasing temperature expands it. The speaker questions the validity of this linearized equation and its relation to evaluating the internal energy.
JackPunchedJi
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.

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.

## 1. What is the equation of state for solids?

The equation of state for solids is a mathematical expression that relates the state variables of a solid, such as temperature, pressure, and volume, to one another. It describes the behavior of a solid under different conditions, and can be used to predict its properties.

## 2. How is the equation of state for solids different from that of gases?

The equation of state for solids is different from that of gases because solids have a fixed volume and do not expand to fill their containers like gases do. This means that the pressure and volume terms in the equation of state for solids are not as closely related as they are for gases.

## 3. Why is the equation of state for solids important in materials science?

The equation of state for solids is important in materials science because it allows scientists to understand and predict the behavior of different materials under various conditions. This is crucial for developing new materials with specific properties, as well as for studying the properties of existing materials.

## 4. Can the equation of state for solids be used for all types of solids?

No, the equation of state for solids cannot be used for all types of solids. It is most accurate for dense, non-porous solids, such as metals and ceramics. It may not be as accurate for porous materials or materials with complex structures, such as polymers.

## 5. How is the equation of state for solids determined experimentally?

The equation of state for solids can be determined experimentally by measuring the state variables of a solid, such as temperature, pressure, and volume, under different conditions. These measurements are then used to fit the data to a mathematical equation that describes the behavior of the solid.

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