What fraction of air is expelled out if a flask containing V litre gas is heated from `27^@C` to `327^@C` ?

Options

A. 0.25
B. 0.5
C. 0.75
D. 0.1

Answer

To solve the problem of how much fraction of air is expelled from a flask when the gas inside is heated from \(27^\circ C\) to \(327^\circ C\), we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant.

### Step-by-Step Solution:

1. **Convert Temperatures to Kelvin:**
- The initial temperature \(T_1\) is \(27^\circ C\).
- To convert to Kelvin:
\[ T_1 = 27 + 273 = 300 \, K \]
- The final temperature \(T_2\) is \(327^\circ C\).
- To convert to Kelvin:
\[ T_2 = 327 + 273 = 600 \, K \]

2. **Use Charles's Law:**
- According to Charles's Law:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Here, \(V_1\) is the initial volume \(V\) and \(V_2\) is the final volume we need to find.
- Plugging in the values:
\[ \frac{V}{300} = \frac{V_2}{600} \]

3. **Solve for \(V_2\):**
- Cross-multiply to find \(V_2\):
\[ V_2 = V \cdot \frac{600}{300} = V \cdot 2 = 2V \]

4. **Calculate the Volume of Air Expelled:**
- The volume of air expelled is the difference between the final volume and the initial volume:
\[ \text{Volume expelled} = V_2 - V_1 = 2V - V = V \]

5. **Calculate the Fraction of Air Expelled:**
- The fraction of air expelled is given by:
\[ \text{Fraction expelled} = \frac{\text{Volume expelled}}{\text{Total volume after heating}} = \frac{V}{2V} = \frac{1}{2} \]

### Final Answer:
The fraction of air expelled is \(\frac{1}{2}\).

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