An iron railway track is installed in winter at an average temperature of 18^ C . The track is made up of 12.0 m sections placed consecutively. What gap must be provided between two adjacent sections to prevent compression in summer, when the peak temperature reaches 48^ C ? The coefficient of linear expansion for iron is 11 10⁻⁶^ C ⁻¹ .

Step-by-step solution

The gap to be provided between two adjacent sections must be equal to the expansion of one section to prevent compression. The initial length of the track section is L = 12.0 m . The change in temperature is T = 48^ C - 18^ C = 30^ C . The coefficient of linear expansion is = 11 10⁻⁶^ C ⁻¹ . The increase in length of one section is given by: L = L T Substituting the given values: L = 12.0 11 10⁻⁶ 30 L = 3960 10⁻⁶ m L = 3.96 10⁻³ m Converting to centimeters: L = 0.396 cm Thus, a gap of 0.396 cm must be provided.