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

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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

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

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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.

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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.anuttarasammyak said:

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.

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So is it just a matter of definition?Chestermiller said:

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.Chestermiller said:

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I would tell more about this implicationmohamed_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

[tex]\alpha(T,p)=(\frac{\partial \log \frac{V}{V_0}}{\partial T})_p[/tex]

where ##V_0## is volume with temperature ##T=T_0##

For simplicity of notion under the condition p=const. through the discussion

[tex]\alpha(T)=\frac{d \log \frac{V}{V_0}}{d T}[/tex]

It is integrated to be

[tex]V=V_0 e^{\int_{T_0}^T \alpha(T)dt}[/tex]

In case ##\alpha## is constant

[tex]V=V_0 e^{\alpha (T-T_0)}[/tex]

Further when ##\alpha (T-T_0) << 1##

[tex]V=V_0 (1+\alpha (T-T_0))[/tex]

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.

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thanks for your generosity. the explanation is amazing and it deepened my understandinganuttarasammyak said:I would tell more about this implication

of definition

[tex]\alpha(T,p)=(\frac{\partial \log \frac{V}{V_0}}{\partial T})_p[/tex]

where ##V_0## is volume with temperature ##T=T_0##

For simplicity of notion under the condition p=const. through the discussion

[tex]\alpha(T)=\frac{d \log \frac{V}{V_0}}{d T}[/tex]

It is integrated to be

[tex]V=V_0 e^{\int_{T_0}^T \alpha(T)dt}[/tex]

In case ##\alpha## is constant

[tex]V=V_0 e^{\alpha (T-T_0)}[/tex]

Further when ##\alpha (T-T_0) << 1##

[tex]V=V_0 (1+\alpha (T-T_0))[/tex]

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.

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.

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.

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.

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.

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.

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