Physics

Problem

Aluminium has an initial density of

2.70\times10^{3}\,\text{kg m}^{-3}

20\,^{\circ}\!\text{C}

. Its coefficient of cubical expansion is

75\times10^{-6}\,\text{K}^{-1}

. (i) Derive an expression for the percentage change in density of aluminium when its temperature is raised by

\Delta T

. (ii) Using the expression obtained in part (i), calculate the temperature rise required to produce a

0.50\%

decrease in the density of aluminium. (iii) What will be the density of aluminium after this temperature rise?