A railway track (made of iron) is laid in winter when the average temperature is `18^(@)C`. The track consists of sections of `12.0 m` placed one after the other. How much gap (in `mum`) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to `48^(@)C`? Coefficient of linear expansion of iron `= 11 xx 10^(-6)//^@C`.

Explanation

To solve the problem of determining the gap that should be left between two sections of a railway track made of iron, we will use the concept of linear expansion. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Length of each section of the railway track, \( L = 12.0 \, \text{m} \)
- Initial temperature, \( T_1 = 18^\circ \text{C} \)
- Final temperature, \( T_2 = 48^\circ \text{C} \)
- Coefficient of linear expansion of iron, \( \alpha = 11 \times 10^{-6} \, \text{°C}^{-1} \)

### Step 2: Calculate the change in temperature
The change in temperature \( \Delta T \) can be calculated as:
\[ \Delta T = T_2 - T_1 = 48^\circ \text{C} - 18^\circ \text{C} = 30^\circ \text{C} \]

### Step 3: Use the formula for linear expansion
The formula for linear expansion is given by:
\[ \Delta L = L \times \alpha \times \Delta T \]
Substituting the known values:
\[ \Delta L = 12.0 \, \text{m} \times (11 \times 10^{-6} \, \text{°C}^{-1}) \times 30 \, \text{°C} \]

### Step 4: Perform the calculation
Calculating \( \Delta L \):
\[ \Delta L = 12.0 \times 11 \times 10^{-6} \times 30 \]
\[ \Delta L = 12.0 \times 330 \times 10^{-6} = 3960 \times 10^{-6} \, \text{m} \]
\[ \Delta L = 0.00396 \, \text{m} = 0.396 \, \text{cm} \]

### Step 5: Convert to micrometers
To find the gap in micrometers (mum), we convert centimeters to micrometers:
\[ 0.396 \, \text{cm} = 0.396 \times 10^4 \, \mu\text{m} = 3960 \, \mu\text{m} \]

### Final Answer
The gap that should be left between two sections of the railway track is **3960 µm**.

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