Physics

Physics

Problem

A rectangular aluminium plate measures 20 cm×30 cm20\,\text{cm} \times 30\,\text{cm} at 20 ∘C20\,^{\circ}\text{C}. The coefficient of superficial expansion of aluminium is β=4.4×10−5 K−1\beta = 4.4 \times 10^{-5}\,\text{K}^{-1}. The plate is heated uniformly to 120 ∘C120\,^{\circ}\text{C}. (i) Calculate its area at 20 ∘C20\,^{\circ}\text{C}. (ii) Determine the increase in its area on heating. (iii) Find the percentage increase in area of the plate.
Intuitive explanation

Thermal expansion of solids depends on how much the temperature changes and a material-specific expansion coefficient. The key insight is that when a solid expands uniformly in all directions, its linear dimensions grow by a small fraction, and the area grows by roughly twice that fraction—this is what the superficial (area) expansion coefficient β\beta captures. You'll use the formula ΔA=βA0ΔT\Delta A = \beta A_0 \Delta T to find how much area is gained, then compare it to the original.

Intuitive explanation

Thermal expansion of solids depends on how much the temperature changes and a material-specific expansion coefficient. The key insight is that when a solid expands uniformly in all directions, its linear dimensions grow by a small fraction, and the area grows by roughly twice that fraction—this is what the superficial (area) expansion coefficient β\beta captures. You'll use the formula ΔA=βA0ΔT\Delta A = \beta A_0 \Delta T to find how much area is gained, then compare it to the original.

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