300 ml of a gas at 300 K is cooled to 276 K at constant pressure. The final volume is

Options

A. 540 ml
B. 276 ml
C. 350 ml
D. 135 ml

Explanation

To solve the problem of finding the final volume of a gas when it is cooled at constant pressure, we can use Charles's Law. Here's a step-by-step solution:

### Step 1: Understand Charles's Law
Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant. Mathematically, this can be represented as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
where:
- \( V_1 \) = initial volume
- \( T_1 \) = initial temperature (in Kelvin)
- \( V_2 \) = final volume
- \( T_2 \) = final temperature (in Kelvin)

### Step 2: Identify the Given Values
From the problem, we have:
- Initial volume, \( V_1 = 300 \, \text{ml} \)
- Initial temperature, \( T_1 = 300 \, \text{K} \)
- Final temperature, \( T_2 = 276 \, \text{K} \)

### Step 3: Rearrange the Equation
We need to find \( V_2 \). Rearranging the equation gives us:
\[ V_2 = V_1 \times \frac{T_2}{T_1} \]

### Step 4: Substitute the Values
Now, substitute the known values into the rearranged equation:
\[ V_2 = 300 \, \text{ml} \times \frac{276 \, \text{K}}{300 \, \text{K}} \]

### Step 5: Calculate the Final Volume
Now perform the calculation:
\[ V_2 = 300 \, \text{ml} \times \frac{276}{300} \]
\[ V_2 = 300 \, \text{ml} \times 0.92 \]
\[ V_2 = 276 \, \text{ml} \]

### Conclusion
The final volume of the gas when cooled to 276 K at constant pressure is:
\[ \boxed{276 \, \text{ml}} \]

---