# Proving coefficient of volume expansion

• bray d
In summary, the conversation discusses the task of proving the equation B=3A, where B and A represent the coefficients of volume and linear expansion, respectively. The conversation includes considerations for a cube with side length 's' and volume V=s^3 undergoing a small temperature change 'dT' and corresponding changes in length and volume 'ds' and 'dV'. The use of the ideal gas law is mentioned but ultimately not applicable. The conversation concludes with a suggested approach to proving the relationship between the two coefficients.
bray d

## Homework Statement

Prove the equation B=3A, where B is the coefficient of volume expansion and A is the coefficient of linear expansion, considering a cube of side 's' and therefore volume V=s^3 that undergoes a small temperature change 'dT' and corresponding length and volume changes 'ds' and 'dV'.

## Homework Equations

B=(deltaV/V)/deltaT
A=(deltaL/L)/deltaT

## The Attempt at a Solution

I think I need to prove the coefficient of linear expansion, then prove the coefficient of volume expansion and observe the relationship between the two. I don't know where to start though, or if there is a more straight forward way. any help is appreciated, thanks

I was thinking of using the ideal gas law:
PV=nRT

but ITS NOT A GAS. I'm lost

Are you sure that you don't just need to show that if the coefficient of linear expansion is A then the coefficient of volume of expansion is just 3A?

I feel that this is more likely the question being asked.

## What is the coefficient of volume expansion?

The coefficient of volume expansion is a measure of how much a material's volume changes in response to a change in temperature. It is typically represented by the symbol α and is expressed in units of 1/K (kelvin).

## Why is it important to prove the coefficient of volume expansion?

Proving the coefficient of volume expansion is important for understanding how a material will behave when exposed to changes in temperature. It can also be useful in designing and engineering systems that require precise dimensional stability.

## What factors affect the coefficient of volume expansion?

The coefficient of volume expansion is primarily affected by the material's atomic structure and bonding. Materials with stronger intermolecular forces tend to have lower coefficients of volume expansion, while materials with weaker forces tend to have higher coefficients.

## How is the coefficient of volume expansion experimentally determined?

The coefficient of volume expansion can be determined experimentally by measuring the change in volume of a material as it is heated or cooled over a known temperature range. This data is then used to calculate the coefficient of volume expansion.

## Can the coefficient of volume expansion be negative?

Yes, the coefficient of volume expansion can be negative. This means that the material actually contracts in volume as it is heated, rather than expanding. This is rare, but can occur in certain materials such as water at very low temperatures.

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