At what centigrade temperature will the volume of a gas at `0^@C` triple itself if the pressure remains constant ?

Explanation

To solve the problem of determining at what centigrade temperature the volume of a gas at 0°C will triple itself while keeping the pressure constant, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial volume \( V_1 = V \)
- Initial temperature \( T_1 = 0°C \)

2. **Convert Initial Temperature to Kelvin**:
- The temperature in Kelvin is given by the formula:
\[ T(K) = T(°C) + 273 \]
- Therefore,
\[ T_1 = 0 + 273 = 273 \, K \]

3. **Determine Final Volume**:
- The final volume \( V_2 \) is three times the initial volume:
\[ V_2 = 3V \]

4. **Apply Charles's Law**:
- According to Charles's Law, at constant pressure, the relationship between volume and temperature is:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

5. **Substitute Known Values into Charles's Law**:
- Plugging in the known values:
\[ \frac{V}{273} = \frac{3V}{T_2} \]

6. **Cancel Out Volume**:
- Since \( V \) is common in both the numerator and denominator, we can cancel it out:
\[ \frac{1}{273} = \frac{3}{T_2} \]

7. **Cross-Multiply to Solve for \( T_2 \)**:
- Cross-multiplying gives:
\[ T_2 = 3 \times 273 \]
- Calculate \( T_2 \):
\[ T_2 = 819 \, K \]

8. **Convert Kelvin to Celsius**:
- To convert the temperature back to Celsius:
\[ T(°C) = T(K) - 273 \]
- Therefore,
\[ T_2(°C) = 819 - 273 = 546 \, °C \]

### Final Answer:
The temperature at which the volume of the gas will triple itself is **546°C**.