Physics 2003 JAMB Past Questions - Question 20: On a fairly cool rainy day when the temperature is 20°C, the length of a steel railroad track is 20m. What will be its length on a hot dry day when the temperature is 40°C?

Correct Answer

C

Explanation

The length of a material like steel can change with temperature because it expands when heated and contracts when cooled. The change in length of a material with temperature is governed by its coefficient of linear expansion (α).

The formula for calculating the change in length (ΔL) of a material with temperature change (ΔT) is given by:

ΔL = L0 * α * ΔT

Where:
ΔL = Change in length
L0 = Initial length (20 meters in this case)
α = Coefficient of linear expansion of the material
ΔT = Change in temperature (in degrees Celsius)

The coefficient of linear expansion for steel can vary depending on the type of steel, but it's typically in the range of around 11 x 10^-6 per degree Celsius.

In this case, the initial temperature is 20°C, and the final temperature is 40°C, so the change in temperature (ΔT) is:

ΔT = 40°C - 20°C = 20°C

Now, we can calculate the change in length (ΔL) using the coefficient of linear expansion for steel:

ΔL = 20m * (11 x 10^-6/°C) * 20°C

ΔL = 20m * 0.00022

ΔL = 0.0044 meters

So, the steel railroad track will expand by 0.0044 meters (or 4.4 millimeters) when the temperature increases from 20°C to 40°C on a hot dry day. Its final length on the hot day would be 20.0044 meters.