If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} C$,then find its coefficient of linear expansion.

Each side of a cubic metal box is $a$ at room temperature $T$. The coefficient of linear expansion of the metal sheet is $\alpha$. The metal box is heated uniformly by a small temperature $\Delta T$,so that its new temperature is $T + \Delta T$. Calculate the increase in the volume of the metal box.

The focal length of a spherical mirror made of steel is $150 \,cm$. If the temperature of the mirror increases by $200 \,K$, its focal length becomes (coefficient of linear expansion of steel $\alpha = 12 \times 10^{-6} \,^{\circ}C^{-1}$). (in $\,cm$)

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times 10^{-5} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

At some temperature $T$,a bronze pin is slightly too large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when: