# What is the relationship between area and volume expansivity? That is what is the formula...

## Question:

What is the relationship between area and volume expansivity? That is what is the formula connecting area and volume expansivity?

## Heat Effect:

The heat energy gained by a substance of a considered system results in higher kinetic energy due to the rapid movement of the constituent particles. The increase in kinetic energy means more separation between the constituent particles and hence we can conclude that the material expands on heating. The expansion can be of three types pertaining to linearl-wise, area-wise and volume-wise of the material.

The expansion of solid in terms of area wise is,

{eq}\dfrac{\Delta A}{A_0} = 2\;\alpha\;\Delta T.........(1)\\ \rm where,\\ \Delta A \rightarrow \textrm{area expansion of the material}\\ A_0 \rightarrow \textrm{original area of the material}\\ \alpha \rightarrow \textrm{coefficient of thermal conductivity}\\ \Delta T \rightarrow \textrm{transition in temperature} {/eq}

Similarly, the expansion of solid in terms of volume-wise is,

{eq}\dfrac{\Delta V}{V_0} = 3\;\rm \alpha \;\Delta\;T.............(2) {/eq}

Since the coefficient of thermal conductivity and transition in temperature can be arbitrarily taken same, therefore, replacing the product of {eq}\alpha \; \Delta\; T {/eq} in either of the two aforementioned equations we get,

In (1),

{eq}\dfrac{\Delta \;A}{A_0} = \dfrac{2}{3}\;\left( \dfrac{\Delta \;V}{V_0}\right)\\ \dfrac{\dfrac{\Delta \;A}{A_0}}{ \dfrac{\Delta \;V}{V_0}} = 1.5 {/eq}