A brass cube has a density of at

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A brass cube has a density of

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

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

. The coefficient of cubical expansion of brass is

6.0\times10^{-5}\,\text{K}^{-1}

. The cube is heated uniformly to

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

. (a) Show that the density

\rho_T

of a solid at temperature

T

can be related to its initial density

\rho_0

at temperature

T_0

by an expression of the form

\rho_T=\dfrac{\rho_0}{1+\gamma\,\Delta T}

, where the symbols have their usual meanings. (b) Using the result of part (a), calculate the density of the brass cube at

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

. (c) Determine the percentage decrease in density produced by this rise in temperature.