On a fairly cool rainy day when the temperature is 20oC, the length of a steel railroad track is 20m. What will be its length on a hot a dry day when the te...
Question 1 Report
On a fairly cool rainy day when the temperature is 20oC, the length of a steel railroad track is 20m. What will be its length on a hot a dry day when the temperature is 40oC?
[coefficient of linear expansion of steel = 11 x 10-6K-1]
Answer Details
The length of a steel railroad track changes with temperature due to thermal expansion or contraction. When the temperature increases, the length of the track will also increase. The amount of expansion depends on the coefficient of linear expansion of steel, which is given in the question as 11 x 10^-6 K^-1.
To find the new length of the track on a hot and dry day, we can use the formula:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.
In this case, the original length L is 20 meters, the change in temperature ΔT is (40-20) = 20 degrees Celsius, and the coefficient of linear expansion α is 11 x 10^-6 K^-1.
Substituting these values into the formula, we get:
ΔL = (11 x 10^-6 K^-1) x (20m) x (20°C) = 0.0044m
Therefore, the new length of the track on the hot and dry day is:
L' = L + ΔL = 20m + 0.0044m = 20.004m
So the answer is 20.004m.
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