# Thermodynamic constant -- misunderstanding

• I
• mohamed_a
In summary, Thermodynamics constants are defined as the coefficients of volumetric thermal expansion and bulk compliance. The V's are included because they are conventions and they vary with both temperature and pressure. By dividing by V, physical dimensions or units of dotted ##\alpha,\beta## become simple, i.e. ##T^{-1},P^{-1}.## Now dotted ##\alpha,\beta## do not depend on volume of the system e.g. 200 ml or 400 ml of volume prepared in the experiments do not matter for measurement of these constants. However, by omitting the V, the coefficient of volumetric thermal expansion would be more intuitive, for example alpha being meter cube

#### mohamed_a

I was reading about thermodynamics in my textbook wheni came across the following thermodynamics constants:

However, i don't understand why did we define 1/V inthe constants. What is the point in doing this?

By dividing by V, physical dimensions or units of dotted ##\alpha,\beta## become simple, i.e. ##T^{-1},P^{-1}.##
Now dotted ##\alpha,\beta## do not depend on volume of the system e.g. 200 ml or 400 ml of volume prepared in the experiments do not matter for measurement of these constants.

##\dot{\alpha}## and ##\dot{\beta}## are not constants. They vary (typically gradually) with both temperature and pressure. However, the V's are included in these definitions because ##\dot{\alpha}## is what we conventionally define as the coefficient of volumetric thermal expansion and ##\dot{\beta}## is what we conventionally define as the bulk compliance of a material (the reciprocal of the bulk modulus).

vanhees71
anuttarasammyak said:
By dividing by V, physical dimensions or units of dotted ##\alpha,\beta## become simple, i.e. ##T^{-1},P^{-1}.##
Now dotted ##\alpha,\beta## do not depend on volume of the system e.g. 200 ml or 400 ml of volume prepared in the experiments do not matter for measurement of these constants.
i still can't find a use of this .So, omitting the V would just make the coefficient more intuitive, for example alpha being meter cube/ kelvin this points more to a rate which makes more sense.

Why would your method be better than giving the % change in volume per unit change in temperature? Besides, your method would depend on the initial volume, and this definition wouldn't. Plus, their definition gives a value that is much more constant than yours does. Do you really think you are smarter than these brilliant scientists who worked this out and studied it over the past few hundred years?

Lord Jestocost and vanhees71
Chestermiller said:
##\dot{\alpha}## and ##\dot{\beta}## are not constants. They vary (typically gradually) with both temperature and pressure. However, the V's are included in these definitions because ##\dot{\alpha}## is what we conventionally define as the coefficient of volumetric thermal expansion and ##\dot{\beta}## is what we conventionally define as the bulk compliance of a material (the reciprocal of the bulk modulus).
So is it just a matter of definition?
Chestermiller said:
Why would your method be better than giving the % change in volume per unit change in temperature? Besides, your method would depend on the initial volume, and this definition wouldn't. Plus, their definition gives a value that is much more constant than yours does. Do you really think you are smarter than these brilliant scientists who worked this out and studied it over the past few hundred years?
that's a probing question not an objection because i couldn't grasp the intuition. However, i understood it when i read wikipedia's page about it. the problem is i didn't understand its meaning because i didn't apply it on an example.

mohamed_a said:
i still can't find a use of this .So, omitting the V would just make the coefficient more intuitive, for example alpha being meter cube/ kelvin this points more to a rate which makes more sense.
of definition
$$\alpha(T,p)=(\frac{\partial \log \frac{V}{V_0}}{\partial T})_p$$
where ##V_0## is volume with temperature ##T=T_0##
For simplicity of notion under the condition p=const. through the discussion
$$\alpha(T)=\frac{d \log \frac{V}{V_0}}{d T}$$
It is integrated to be
$$V=V_0 e^{\int_{T_0}^T \alpha(T)dt}$$
In case ##\alpha## is constant
$$V=V_0 e^{\alpha (T-T_0)}$$
Further when ##\alpha (T-T_0) << 1##
$$V=V_0 (1+\alpha (T-T_0))$$
We can make use of thus defined ##\alpha## to express thermal expansion nature of matter in such a way. I hope you would share its convenience with us.

Last edited:
vanhees71 and mohamed_a
anuttarasammyak said:
of definition
$$\alpha(T,p)=(\frac{\partial \log \frac{V}{V_0}}{\partial T})_p$$
where ##V_0## is volume with temperature ##T=T_0##
For simplicity of notion under the condition p=const. through the discussion
$$\alpha(T)=\frac{d \log \frac{V}{V_0}}{d T}$$
It is integrated to be
$$V=V_0 e^{\int_{T_0}^T \alpha(T)dt}$$
In case ##\alpha## is constant
$$V=V_0 e^{\alpha (T-T_0)}$$
Further when ##\alpha (T-T_0) << 1##
$$V=V_0 (1+\alpha (T-T_0))$$
We can make use of thus defined ##\alpha## to express thermal expansion nature of matter in such a way. I hope you would share its convenience with us.
thanks for your generosity. the explanation is amazing and it deepened my understanding

Delta2, Chestermiller and anuttarasammyak

## What is a thermodynamic constant and why is it important?

A thermodynamic constant is a value that remains constant regardless of changes in temperature, pressure, or other conditions. These constants are important because they help us understand how different substances behave under different conditions and can be used to predict the behavior of a system.

## What is a common misunderstanding about thermodynamic constants?

A common misunderstanding about thermodynamic constants is that they are always the same for all substances. In reality, these constants can vary depending on the substance and the conditions in which it is being measured.

## Can thermodynamic constants change?

Yes, thermodynamic constants can change depending on the conditions in which they are measured. For example, the specific heat capacity of a substance can vary with temperature and pressure.

## What is the difference between a thermodynamic constant and a thermodynamic property?

A thermodynamic constant is a fixed value, while a thermodynamic property is a measurable characteristic of a substance that can vary depending on the conditions. Thermodynamic constants are often used to calculate thermodynamic properties.

## How are thermodynamic constants determined?

Thermodynamic constants are typically determined through experiments or theoretical calculations. These values are then used in equations to predict the behavior of a system under different conditions.