Question

Obtain an expression for the variation of the density of a solid with temperature.

Answer 1

Density, = \(\rho\) = \(\cfrac{mass}{volume}\)

∴ \(\rho_1\) = \(\cfrac{mass}{V_1}\) and \(\rho_2\) = \(\cfrac{mass}{V_2}\)

∴ \(\cfrac{​​\rho_1}{​​​​\rho_2}\) = \(\cfrac{V_2}{V_1}\) = 1 + \(\beta\) ΔT

∴ \(\rho_2\) = \(\cfrac{​​\rho_1}{​​​​1+\betaΔT}\)

As the temperature increases, density decreases.