At what temperature on Celsius scale will the volume of a given mass of a gas at `0^(@)C` become half of its volume at constant pressure?

Explanation

To solve the problem of finding the temperature at which the volume of a given mass of gas at 0°C becomes half of its original volume at constant pressure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- We have an initial temperature \( T_1 = 0°C \).
- The volume at this temperature is \( V_1 \).
- The final volume \( V_2 \) is half of \( V_1 \), so \( V_2 = \frac{V_1}{2} \).

2. **Convert Celsius to Kelvin**:
- The initial temperature in Kelvin is:
\[ T_1 = 0°C + 273 = 273 \, K \]

3. **Use the Ideal Gas Law**:
- According to the ideal gas law, at constant pressure, the relationship between volume and temperature can be expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Here, \( T_2 \) is the final temperature we need to find.

4. **Substitute Known Values**:
- Substitute \( V_2 = \frac{V_1}{2} \) and \( T_1 = 273 \, K \) into the equation:
\[ \frac{V_1}{273} = \frac{\frac{V_1}{2}}{T_2} \]

5. **Simplify the Equation**:
- Cancel \( V_1 \) from both sides (assuming \( V_1 \neq 0 \)):
\[ \frac{1}{273} = \frac{1/2}{T_2} \]
- Cross-multiply to solve for \( T_2 \):
\[ T_2 = \frac{273 \times 1}{\frac{1}{2}} = 273 \times 2 = 546 \, K \]

6. **Convert Kelvin Back to Celsius**:
- To convert \( T_2 \) back to Celsius:
\[ T_2 = 546 \, K - 273 = 273 \, °C \]

### Final Answer:
The temperature at which the volume of the gas becomes half of its original volume at constant pressure is \( 273 \, °C \).