Physics

Physics

Problem

A steel rail of length 30 m30\,\text{m} has a coefficient of linear expansion α=12×10−6 K−1\alpha = 12\times10^{-6}\,\text{K}^{-1}. Calculate the increase in its length when the temperature rises by 40 ∘C40\,^{\circ}\text{C}. a) 14.4 cm14.4\,\text{cm} b) 0.72 cm0.72\,\text{cm} c) 1.44 cm1.44\,\text{cm} d) 0.144 cm0.144\,\text{cm}
Intuitive explanation

Thermal expansion is about how materials grow when heated—the key is that length change depends on three things: the original length, how much the temperature changes, and the material's sensitivity to heat (its expansion coefficient). You'll use the linear expansion formula ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T, where each factor plays a direct role in determining how much the rail stretches.

Intuitive explanation

Thermal expansion is about how materials grow when heated—the key is that length change depends on three things: the original length, how much the temperature changes, and the material's sensitivity to heat (its expansion coefficient). You'll use the linear expansion formula ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T, where each factor plays a direct role in determining how much the rail stretches.

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