If `300 ml` of a gas at `27^(@)C` is cooled to `7^(@)C` at constant pressure, then its final volume will be

Options

A. `540 ml`
B. `350 ml`
C. `280 ml`
D. `135 ml`

Explanation

To solve the problem, we will use Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when the pressure is held constant. The formula for Charles's Law can be expressed as:

\[ \frac{V_1}{V_2} = \frac{T_1}{T_2} \]

Where:
- \( V_1 \) is the initial volume of the gas.
- \( V_2 \) is the final volume of the gas.
- \( T_1 \) is the initial temperature in Kelvin.
- \( T_2 \) is the final temperature in Kelvin.

### Step-by-Step Solution:

1. **Convert the temperatures from Celsius to Kelvin**:
- The initial temperature \( T_1 \) is \( 27^\circ C \):
\[ T_1 = 27 + 273 = 300 \, K \]
- The final temperature \( T_2 \) is \( 7^\circ C \):
\[ T_2 = 7 + 273 = 280 \, K \]

2. **Identify the initial volume \( V_1 \)**:
- Given \( V_1 = 300 \, ml \).

3. **Apply Charles's Law**:
- Rearranging the formula to find \( V_2 \):
\[ V_2 = V_1 \cdot \frac{T_2}{T_1} \]

4. **Substitute the known values into the equation**:
\[ V_2 = 300 \, ml \cdot \frac{280 \, K}{300 \, K} \]

5. **Calculate \( V_2 \)**:
- Simplifying the equation:
\[ V_2 = 300 \cdot \frac{280}{300} = 280 \, ml \]

Thus, the final volume of the gas after cooling to \( 7^\circ C \) at constant pressure is **280 ml**.