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**[SOLVED] Density Change Caused by Temp. Change**

## Homework Statement

Show that the change in the density [itex]\rho[/itex] of a substance, when the temperature changes by [itex]\Delta T[/itex], is given by [itex]\Delta \rho = - \beta \rho \Delta T[/itex].

## Homework Equations

[tex]\rho = \frac{m}{V}[/tex]

[tex]\Delta V = \beta V \Delta T[/tex]

## The Attempt at a Solution

Let [itex]\rho_1[/itex] and [itex]\rho_2[/itex] be the densities of the substance before and after the temp. change [itex]\Delta T[/itex]. After some algebra, I get:

[tex]\Delta \rho = \rho_2 - \rho_1 = - \beta \rho_2 \Delta T[/tex]

This differs from that given in the problem statements because [itex]\rho[/itex] is [itex]\rho_1[/itex] in the above. I guess this must be typo right?

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