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 what fraction of air is expelled when a flask containing V liters of gas is heated from 27°C to 327°C, we can follow these steps:

### Step 1: Convert Celsius to Kelvin
First, we need to convert the temperatures from Celsius to Kelvin.
- For T1 (27°C):
\[ T1 = 27 + 273 = 300 \, K \]
- For T2 (327°C):
\[ T2 = 327 + 273 = 600 \, K \]

### Step 2: Apply Charles's Law
According to Charles's Law, the volume of a gas is directly proportional to its temperature when pressure is held constant. This can be expressed as:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
Where:
- \( V1 \) is the initial volume (V liters)
- \( V2 \) is the final volume after heating

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ \frac{V}{300} = \frac{V2}{600} \]

### Step 4: Solve for V2
Cross-multiplying gives:
\[ V \cdot 600 = V2 \cdot 300 \]
\[ V2 = \frac{600V}{300} = 2V \]

### Step 5: Calculate the Volume of Air Expelled
The volume of air expelled can be calculated as:
\[ \text{Volume expelled} = V2 - V = 2V - V = V \]

### Step 6: Calculate the Fraction of Air Expelled
To find the fraction of air expelled, we divide the volume expelled by the final volume:
\[ \text{Fraction} = \frac{\text{Volume expelled}}{\text{Final volume}} = \frac{V}{2V} = \frac{1}{2} \]

### Final Answer
The fraction of air expelled when the gas is heated from 27°C to 327°C is:
\[ \frac{1}{2} \text{ or } 0.5 \]

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