The readings of a thermometer at `0^(@)C` and `100^(@)C` are `50 cm` and `75 cm` of mercury column respectively. Find the temperature at which its reading is `80 cm` of mercury column ?

Explanation

To solve the problem step by step, we will use the concept of linear expansion of the mercury column in the thermometer.

### Step 1: Understand the given data
- At \(0^\circ C\), the length of the mercury column, \(L_1 = 50 \, \text{cm}\).
- At \(100^\circ C\), the length of the mercury column, \(L_2 = 75 \, \text{cm}\).
- We need to find the temperature \(T\) at which the length of the mercury column, \(L' = 80 \, \text{cm}\).

### Step 2: Use the linear expansion formula
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