10 g of a gas at NTP occupies a volume of 2 litres. At what temperature will the volume be double , pressure and amount of the gas remaining same ?

Options

A. 273 K
B. 546K
C. `-273^@C`
D. `546^@ C`

Answer

To solve the problem step by step, 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 Given Information:**
- Mass of gas (m) = 10 g
- Initial volume (V1) = 2 liters
- Initial temperature (T1) = 273 K (NTP)
- Final volume (V2) = 2 * V1 = 4 liters (since the volume is to be doubled)

2. **Charles's Law Equation:**
- According to Charles's Law, we can write:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
- Rearranging this gives us:
\[ T2 = \frac{V2 \cdot T1}{V1} \]

3. **Substituting Values:**
- Substitute the known values into the equation:
\[ T2 = \frac{4 \, \text{liters} \cdot 273 \, \text{K}}{2 \, \text{liters}} \]

4. **Calculate T2:**
- Perform the calculation:
\[ T2 = \frac{4 \cdot 273}{2} = \frac{1092}{2} = 546 \, \text{K} \]

5. **Final Answer:**
- The temperature at which the volume will be double, while keeping pressure and the amount of gas constant, is **546 K**.