Expansion is calculated using the formula: e = 1000 x L x α x T   

e = expansion in millimetres 

L = length of free* rail (m)    * note “free rail” means un-clipped and unrestricted to move lengthwise 

α = coefficient of linear expansion = 0.0000115 

T = difference between actual temperature and 27 °C     i.e.  (27°C – rail temperature) 

Extension (e) = Length of rail in metres (L) x coefficient of linear expansion (α) x difference between actual temperature and 27 °C (T) 

 

Q1) Calculate extension of 125 metres of rail at 20°C 

 

125x 0.0115 x 7 =  

 

Q2) Calculate extension of 275 metres of rail at 12°C 

 

275 x 0.0115 x 15 =  

 

Q3) Calculate extension of 300 metres of rail at 15°C 

300 x 0.0115 x 12 =  

Let's calculate the extension for each of the scenarios provided using the formula:

\[
e = 1000 \times L \times \alpha \times T
\]

Where:
- \( L \) is the length of the rail in meters.
- \( \alpha = 0.0000115 \) is the coefficient of linear expansion.
- \( T = 27°C - \text{rail temperature} \) is the temperature difference.

### Q1) Extension for 125 meters of rail at 20°C

First, calculate \( T \):

\[
T = 27°C - 20°C = 7°C
\]

Then, calculate the extension \( e \):

\[
e = 1000 \times 125 \times 0.0000115 \times 7
\]

\[
e = 1000 \times 125 \times 0.0000805 = 1000 \times 0.100625 = 100.625 \text{ mm}
\]

### Q2) Extension for 275 meters of rail at 12°C

First, calculate \( T \):

\[
T = 27°C - 12°C = 15°C
\]

Then, calculate the extension \( e \):

\[
e = 1000 \times 275 \times 0.0000115 \times 15
\]

\[
e = 1000 \times 275 \times 0.0001725 = 1000 \times 0.474375 = 474.375 \text{ mm}
\]

### Q3) Extension for 300 meters of rail at 15°C

First, calculate \( T \):

\[
T = 27°C - 15°C = 12°C
\]

Then, calculate the extension \( e \):

\[
e = 1000 \times 300 \times 0.0000115 \times 12
\]

\[
e = 1000 \times 300 \times 0.000138 = 1000 \times 0.414 = 414 \text{ mm}
\]

### Summary of Results:
1. **Extension for 125 meters at 20°C:** \( 100.625 \) mm
2. **Extension for 275 meters at 12°C:** \( 474.375 \) mm
3. **Extension for 300 meters at 15°C:** \( 414 \) mm

Would you like more details or have any other questions? Here are some related questions you might be interested in:

1. How would the extension change if the rail temperature were 30°C instead of 20°C?
2. What would be the extension for a 400-meter rail at 10°C?
3. How does the coefficient of linear expansion (\( \alpha \)) affect the extension calculation?
4. What happens to the rail if the temperature difference \( T \) becomes negative?
5. Can this formula be used for materials other than steel, and how would \( \alpha \) change?

**Tip:** Remember that the coefficient of linear expansion \( \alpha \) is specific to the material and is crucial in determining how much the material will expand or contract with temperature changes.

Learn how to calculate rail expansion using the linear expansion formula e = 1000 * L * α * T. This problem involves determining the extension of rails at different temperatures using the coefficient of linear expansion. Suitable for professionals needing to understand dimensional changes due to temperature variations.

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