An open flask contains air at 27°C.To what temperature it must be heated to expel one-fourth of the air?

Options

A. 127°C
B. 65°C
C. 927°C
D. 460°C

Answer

To solve the problem of determining the temperature to which an open flask containing air at 27°C must be heated to expel one-fourth of the air, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- The initial temperature \( T_1 \) is given as 27°C.
- Convert this temperature to Kelvin:
\[ T_1 = 27 + 273 = 300 \, \text{K} \]

2. **Determine the Moles of Air**:
- Let the initial number of moles of air in the flask be \( n \).
- If one-fourth of the air is expelled, the remaining moles of air will be:
\[ n_2 = n - \frac{1}{4}n = \frac{3}{4}n \]

3. **Apply the Ideal Gas Law**:
- According to the ideal gas law, for a constant pressure and volume, the product of the number of moles and temperature remains constant:
\[ n_1 T_1 = n_2 T_2 \]
- Here, \( n_1 = n \), \( T_1 = 300 \, \text{K} \), and \( n_2 = \frac{3}{4}n \).

4. **Substitute Values into the Equation**:
- Substitute the known values into the equation:
\[ n \cdot 300 = \frac{3}{4}n \cdot T_2 \]
- Cancel \( n \) from both sides (assuming \( n \neq 0 \)):
\[ 300 = \frac{3}{4} T_2 \]

5. **Solve for \( T_2 \)**:
- Rearranging the equation to find \( T_2 \):
\[ T_2 = \frac{300 \times 4}{3} = 400 \, \text{K} \]

6. **Convert \( T_2 \) Back to Celsius**:
- Convert the temperature from Kelvin back to Celsius:
\[ T_2 = 400 - 273 = 127 \, \text{°C} \]

### Final Answer:
The temperature to which the flask must be heated to expel one-fourth of the air is **127°C**.

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