A constant volume gas thermometer shows pressure readings of `50 cm` and `90 cm` of mercury at `0^(0)C` and `100^(0)C` respectively. What is the temperature on gas scale when the pressure reading is `60 cm` of mercury ?

Explanation

To solve the problem step by step, we will use the relationship between the pressure readings of the gas thermometer and the corresponding temperatures.

### Step 1: Identify the known values
We know the following pressure readings at specific temperatures:
- At \(0^{\circ}C\), the pressure \(P_0 = 50 \, \text{cm of mercury}\)
- At \(100^{\circ}C\), the pressure \(P_{100} = 90 \, \text{cm of mercury}\)

We need to find the temperature \(T\) when the pressure reading \(P_t = 60 \, \text{cm of mercury}\).
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