A bridge is made with segments of concrete 50 m long. If the linear expansion coefficient is 12 × 10−⁶ (°C)−¹, how much spacing (in cm) is needed to allow for expansion during an extreme temperature change of 150° F? A) 10 B) 2.5 C) 7.5 D) 5.0 E) 9.5

Question

Quizplus · Accepted Answer

To calculate the spacing needed for expansion, use the formula for linear expansion: ΔL = αLΔT, where ΔL is the change in length, α is the linear expansion coefficient, L is the original length, and ΔT is the temperature change. First, convert the temperature change from Fahrenheit to Celsius, since the coefficient is per degree Celsius. ΔT(°C) = (150°F - 32) × 5/9 = 65.56°C. Then, ΔL = (12 × 10^-6 /°C) × 50 m × 65.56°C = 0.039336 m or 3.9336 cm. The closest answer is 5.0 cm, allowing some extra space for safety.

A Bridge Is Made with Segments of Concrete 50 M