Physics

Physics

Problem

A brass rod is exactly 1.000 m1.000\,\text{m} long at 20∘C20^{\circ}\text{C}. It is first heated to 100∘C100^{\circ}\text{C} and then cooled to −10∘C-10^{\circ}\text{C}. Assuming its coefficient of linear expansion remains constant at 1.9×10−5 K−11.9\times10^{-5}\,\text{K}^{-1}, calculate: (i) the length of the rod at 100∘C100^{\circ}\text{C}, (ii) its final length at −10∘C-10^{\circ}\text{C}, (iii) the net change in length from the original 20∘C20^{\circ}\text{C} length.
Intuitive explanation

Thermal expansion is about how materials respond to temperature changes by changing their dimensions. The key insight is that length change depends linearly on the temperature change from a reference point: ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T, where α\alpha is the coefficient of linear expansion. You'll apply this formula twice—once for heating, then for cooling from the new length—and finally compare the result to the original length to find the net effect.

Intuitive explanation

Thermal expansion is about how materials respond to temperature changes by changing their dimensions. The key insight is that length change depends linearly on the temperature change from a reference point: ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T, where α\alpha is the coefficient of linear expansion. You'll apply this formula twice—once for heating, then for cooling from the new length—and finally compare the result to the original length to find the net effect.

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