Final answer:
The expansion gap that should be left between steel railroad rails laid on a winter day when their temperature is -7.0 °C, and when they may reach a maximum temperature 35.0°C greater than when they were laid, should be at least 0.0504 meters or 50.4 millimeters.
Step-by-step explanation:
The expansion gap that should be left between steel railroad rails can be determined using the formula: ΔL = L * α * ΔT, where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature. In this case, the temperature difference is given as 35.0°C, which is greater than when the rails were laid. So, the temperature change is ΔT = 35.0°C - (-7.0°C) = 42.0°C. Now, we need to find the coefficient of linear expansion, which depends on the material. For steel, the coefficient of linear expansion is approximately α = 1.2 * 10^-5 °C^-1. Therefore, the change in length is ΔL = 10.0 m * 1.2 * 10^-5 °C^-1 * 42.0°C = 0.0504 m. The expansion gap should be at least 0.0504 meters or 50.4 millimeters.