Question

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0°C greater than when they were laid? Their original length is 10.0 m.

(a) 0.087 m
(b) 0.090 m
(c) 0.093 m
(d) 0.097 m

Answer 1

The expansion gap needed between steel railroad rails with an original length of 10.0 m that may reach a temperature 35.0°C higher than when laid is calculated using the formula ΔL = αLΔT. With α approximately 12 x 10-6 °C-1 for steel and a temperature increase of ΔT = 35.0°C, the expansion gap should be at least ΔL = 0.0042 m or 4.2 mm.

Step-by-step explanation:

To determine how large an expansion gap should be left between steel railroad rails that may reach a maximum temperature of 35.0°C greater than when they were laid, we use the linear thermal expansion formula ΔL = αLΔT. In this formula, ΔL is the change in length, α is the coefficient of linear expansion for steel (which is typically around 12 x 10-6 °C-1), L is the original length of the rails, and ΔT is the change in temperature. The original length given is 10.0 m.

Plugging in the numbers:

• α = 12 x 10-6 °C-1
• L = 10.0 m
• ΔT = 35.0°C

ΔL = (12 x 10-6 °C-1)(10.0 m)(35.0°C)

ΔL = 0.0042 m or 4.2 mm

This is the amount that the steel rail will expand and thus is the minimum gap needed to avoid problems related to thermal expansion at the predicted maximum temperature increase.