By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from 24°C to -16°C? The coefficient of linear thermal expansion for this concrete is 1.0 × 10^-5 K^-1. A)0.50 cm B)0.72 cm C)1.2 cm D)1.5 cm

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Quizplus · Accepted Answer

The length change $\Delta L$ due to temperature change can be calculated using the formula $\Delta L = \alpha L_0 \Delta T$, where $\alpha$ is the coefficient of linear expansion, $L_0$ is the original length, and $\Delta T$ is the temperature change. Here, $\alpha = 1.0 \times 10^{-5} / ^\circ C$, $L_0 = 18 m = 1800 cm$ (since 1 m = 100 cm), and $\Delta T = -16^\circ C - 24^\circ C = -40^\circ C$. Thus, $\Delta L = 1.0 \times 10^{-5} \times 1800 \times (-40) = -0.72 cm$. The contraction means the length decreases, so the change is negative, indicating a reduction in length. However, when we talk about the length by which something contracts, we refer to the absolute value, which is $0.72 cm$.

By What Length Will a Slab of Concrete That Is