Question
Why are small gaps left between consecutive sections of railway tracks? Explain using the concept of thermal expansion. If a steel track is 25 m long at 20°C, what gap must be left if the track must not buckle at 60°C? (Coefficient of linear expansion of steel )
Solution — Step by Step
Steel, like all metals, expands when heated. Railway tracks are made of steel and sit in the open, experiencing temperature swings from winter cold to blazing summer heat — easily a range of 40-50°C.
If tracks are laid end-to-end with no gaps, heating causes each section to try to expand. But both ends are constrained by neighbouring sections. The only way the material can “expand” is to buckle sideways — this is called buckling or thermal buckling, and it makes the track dangerous for train operation.
When a material of length at temperature is heated to temperature :
Where:
- = change in length
- = original length
- = coefficient of linear expansion (material-specific)
- = temperature change
Given:
- ,
For the track not to buckle at 60°C, each 25 m section must have room to expand by 1.2 cm. So the minimum gap between adjacent track sections must be 1.2 cm (12 mm).
In practice, railway engineers leave a slightly larger gap to account for extreme temperature conditions and to ensure safety margins.
Why This Works
Every solid material has atoms vibrating about equilibrium positions. When temperature increases, atoms vibrate more vigorously — they effectively need more space, so the average distance between atoms increases. This causes the entire object to expand.
The linear expansion coefficient tells us how much a unit length expands per degree Celsius. For steel, — meaning a 1 m steel rod expands by 0.000012 m (0.012 mm) for every 1°C rise. Over 25 m and 40°C, this accumulates to a noticeable 12 mm.
The gap design is elegant engineering: it accommodates thermal expansion in summer and thermal contraction in winter (tracks shorten in cold weather). Modern railways use continuously welded rail (CWR) where tracks are welded together, but then pre-stressed with enough tension to prevent buckling — the thermal stress is engineered into the system rather than accommodated by gaps.
Alternative Method
We can also think of this in terms of thermal stress — the stress that would develop if expansion were prevented:
For steel, Young’s modulus :
This enormous compressive stress (about 1000 times atmospheric pressure) would easily buckle a track, confirming why gaps are essential in conventional rail design.
This type of question appears regularly in CBSE Class 11 exams and occasionally in JEE. When solving thermal expansion problems, always write down first, then substitute. For JEE, thermal stress problems () also come up — remember to use Young’s modulus, not just linear expansion.
Common Mistake
Students often confuse the coefficient of linear expansion () with the coefficient of volumetric expansion (). For a given material, (volume expands in all three dimensions). For a long thin rail, we use linear expansion (expansion along the length). Using instead of would give a value three times too large. Also, some students forget to convert to the correct sign — if the question asks about cooling (e.g., contraction in winter), is negative, giving a negative (contraction).