Pressure remaining constant, the volume of a given sample of gas at `127^(@)C` will be doubled at

Options

A. `254^(@)C`
B. `527^(@)C`
C. `400K`
D. `800^(@)C`

Answer

To solve the problem, we will use Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin).

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Given initial temperature \( T_1 = 127^\circ C \).
- Convert \( T_1 \) to Kelvin:
\[ T_1 = 127 + 273 = 400 \, K \]
- Let the initial volume be \( V_1 = V \).

2. **Determine Final Volume:**
- The problem states that the volume will be doubled, so:
\[ V_2 = 2V \]

3. **Apply Charles's Law:**
- According to Charles's Law:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Substitute the known values:
\[ \frac{V}{400} = \frac{2V}{T_2} \]

4. **Solve for \( T_2 \):**
- Cross-multiply to find \( T_2 \):
\[ V \cdot T_2 = 2V \cdot 400 \]
- Simplifying gives:
\[ T_2 = 2 \cdot 400 = 800 \, K \]

5. **Convert \( T_2 \) to Celsius:**
- Convert \( T_2 \) back to degrees Celsius:
\[ T_2 = 800 - 273 = 527^\circ C \]

### Final Answer:
The temperature at which the volume of the gas will be doubled is \( 527^\circ C \).