Question

At what temperature will the steel rails, 50 cm long at 10°C, touch each other when the coefficient of linear expansion of steel is 12 x 10^(-6) K^(-1)?

Answer 1

The expansion gap needed between steel rails to accommodate a 35°C temperature increase is calculated using the linear thermal expansion formula, resulting in a gap size of 4.2 mm.

Step-by-step explanation:

The subject of this question is Physics, specifically relating to thermal expansion. The grade level is High School.

To solve for the expansion gap needed between steel railroad rails, we must use the equation for linear thermal expansion, which is ΔL = αLΔT, where:

• ΔL represents the change in length (the expansion gap size we want to find),
• α is the coefficient of linear expansion (12 x 10-6 K-1 for steel),
• L is the original length of the steel rails (10.0 meters),
• ΔT is the change in temperature (35.0°C in this case).

Substituting the known values into the equation gives us:

ΔL = (12 x 10-6 K-1)(10.0 m)(35.0°C) = 0.0042 m or 4.2 mm

This calculation tells us that the expansion gap between the rails should be 4.2 mm to accommodate the expected temperature increase.