Thermal Expansion Of Solids

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A metal rod of length 1 m at 20°C has a coefficient of linear expansion of 2 	imes 10^{-5} per °C; how much does it elongate when heated to 120°C?

RankGuru · Accepted Answer

As described in NCERT Class 11, Chapter 11 (Thermal Properties of Matter), most solids expand on heating, and the change in length is given by $\Delta L = L_0 \alpha \Delta T$, where $\alpha$ is the coefficient of linear expansion and $\Delta T$ the temperature rise. Heating increases the average separation between atoms, lengthening the rod. The temperature change is $\Delta T = 120 - 20 = 100\ ^{\circ}	ext{C}$. Substituting $L_0 = 1\ 	ext{m}$, $\alpha = 2 	imes 10^{-5}\ ^{\circ}	ext{C}^{-1}$ and $\Delta T = 100$ gives $\Delta L = 1 	imes 2 	imes 10^{-5} 	imes 100 = 2 	imes 10^{-3}\ 	ext{m} = 2\ 	ext{mm}$. The option 1 mm uses a temperature rise of only 50°C. The option 4 mm doubles $\alpha$ incorrectly. The option 0.2 mm misplaces a power of ten. As a plausibility check, a millimetre-scale expansion over a metre rod for a 100°C rise is exactly the small but measurable effect that requires expansion gaps in railway tracks and bridges, confirming the answer.

Thermal Expansion Of Solids

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