A bulb contains air at atmospheric pressure at `40^(@)C` temperature. The maximum pressure bulb can withstand is 2 atmosphere. Calculate the temperuatre of air when the bulb is on the point of bursting.

Explanation

To solve the problem, we will use the relationship between pressure and temperature for a gas at constant volume, which is described by the formula:

\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

### Step-by-Step Solution:

1. **Identify Given Values**:
- Initial pressure \( P_1 = 1 \, \text{atm} \) (atmospheric pressure)
- Initial temperature \( T_1 = 40^\circ C \)
- Maximum pressure \( P_2 = 2 \, \text{atm} \) (pressure at bursting point)

2. **Convert Temperature to Kelvin**:
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- Therefore,
\[ T_1 = 40 + 273.15 = 313.15 \, K \approx 313 \, K \]

3. **Set Up the Equation**:
- Using the relationship for isochoric processes:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

4. **Substitute Known Values**:
- Substitute \( P_1 \), \( T_1 \), and \( P_2 \) into the equation:
\[ \frac{1 \, \text{atm}}{313 \, K} = \frac{2 \, \text{atm}}{T_2} \]

5. **Cross-Multiply to Solve for \( T_2 \)**:
- Rearranging gives:
\[ T_2 = \frac{2 \, \text{atm} \times 313 \, K}{1 \, \text{atm}} = 626 \, K \]

6. **Final Result**:
- The temperature of the air when the bulb is on the point of bursting is:
\[ T_2 = 626 \, K \]