Question

The coefficient of linear expansion of the steel in a certain bridge is 1.10 x 10 5/C°. If at a minimum winter temperature of -30°C the bridge is 30.5 m long, at the summer maximum of 40°C its length is increased about

A. 2.54 cm.
B. 2.54 mm.
C. 0.254 mm.
D. 2.54 um
E. 25.4um

Answer 1

The steel bridge expands by approximately 2.31 cm when the temperature rises from -30°C to 40°C, nearest to the given option A. 2.54 cm.

Step-by-step explanation:

To calculate the length increase of a steel bridge due to thermal expansion, we use the formula ∆L = αL₀∆T, where ∆L is the change in length, α is the coefficient of linear expansion of the material, L₀ is the initial length, and ∆T is the change in temperature. In this case, the coefficient of linear expansion (α) for steel is given as 1.10 x 10⁵/C°, the initial length (L₀) is 30.5 m, and the temperature change (∆T) is 70°C, as it changes from -30°C to 40°C. Plugging in these values, we get ∆L = (1.10 x 10⁵/C°)(30.5 m)(70°C).

Calculating that gives us a change in length (∆L) = 0.00231 m, or 2.31 cm. The correct answer for how much the length of the bridge increases in the summer as compared to the winter minimum temperature is thus approximately 2.31 cm, which is nearest to option A. 2.54 cm from the original question set.