Steel rails for a train track are laid in a region subject...

Steel rails for a train track are laid in a region subject to extremes of temperature. The distance from one juncture to the next is $5.2000 \mathrm{~m},$ and the cross-sectional area of the rails is $60 . \mathrm{cm}^{2}$. If the rails touch each other without buckling at the maximum temperature, $50 .{ }^{\circ} \mathrm{C}$, how much space will there be between the rails at $-10 .{ }^{\circ} \mathrm{C} ?$

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Key Concepts

Linear Thermal Expansion

This concept refers to the change in length of a material in response to a change in temperature. It is quantified by the formula ?L = ?L??T, where ?L is the change in length, L? is the original length, ? is the coefficient of linear expansion, and ?T is the change in temperature. This fundamental idea in thermal physics explains how materials expand when heated and contract when cooled.

Coefficient of Thermal Expansion

This is a material-specific constant that measures the relative change in size per degree change in temperature. It plays a crucial role in predicting how much a material will expand or contract over a certain temperature range. Understanding this coefficient is key in engineering applications where temperature variations can lead to significant dimensional changes.

Thermal Tolerances in Engineering

In many engineering designs, structures are built with gaps or tolerances to accommodate the expansion and contraction of materials caused by temperature fluctuations. This is particularly important in applications such as rail tracks, where the design must ensure that the components do not buckle when expanded at higher temperatures and still function correctly at lower temperatures. Understanding how temperature changes affect dimensions helps engineers design safer and more reliable structures.

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