A steel track measures \(25 \mathrm{~m}\) at \(20^{\circ} \mathrm{C}\). At \(70{ }^{\circ} \mathrm{C}\) it measures \(25.01 \mathrm{~m}\). Calculate the percentage change in the length of the track as its temperature changes from \(20^{\circ} \mathrm{C}\) to \(70{ }^{\circ} \mathrm{C}\).

Short Answer

Expert verified
Answer: 0.04%

Step by step solution

01

Calculate the change in length

To find the change in length, we need to subtract the initial length from the final length: Change in length = Final length - Initial length Change in length = 25.01 m - 25 m Change in length = 0.01 m
02

Calculate the percentage change in length

To find the percentage change in length, we will divide the change in length by the initial length and multiply by 100: Percentage change = (Change in length / Initial length) * 100 Percentage change = (0.01 m / 25 m) * 100 Percentage change = 0.0004 * 100 Percentage change = 0.04 % So, the percentage change in the length of the steel track as its temperature changes from 20°C to 70°C is 0.04%.

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