(e) (i) Define linear expansivity of thermal expansion. (1 mark) (ii) A steel wire whose length L is 130 cm is heated to an average 180^circ C .What is the amount the wire shrinks if it is freely allowed to cool to 20^circ C (3 marks)

(i) Linear expansivity of thermal expansion refers to the fractional change in length of a material per unit change in temperature. It is a measure of how much a material expands or contracts per degree change in temperature.<br /><br />(ii) To find the amount the wire shrinks when it cools from $180^{\circ }C$ to $20^{\circ }C$, we can use the formula for linear expansion:<br /><br />$\Delta L = L \cdot \alpha \cdot \Delta T$<br /><br />where:<br />- $\Delta L$ is the change in length,<br />- $L$ is the original length,<br />- $\alpha$ is the linear expansivity of the material, and<br />- $\Delta T$ is the change in temperature.<br /><br />Given:<br />- $L = 130$ cm,<br />- $\alpha$ for steel is approximately $12 \times 10^{-6} / ^{\circ }C$, and<br />- $\Delta T = 180^{\circ }C - 20^{\circ }C = 160^{\circ }C$.<br /><br />Substituting the values into the formula:<br /><br />$\Delta L = 130 \cdot 12 \times 10^{-6} \cdot 160$<br /><br />$\Delta L = 0.0252$ cm<br /><br />Therefore, the wire will shrink by approximately 0.0252 cm when it cools from $180^{\circ }C$ to $20^{\circ }C$.