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 the relationship derived from the ideal gas law. Here’s a step-by-step solution:

### Step 1: Write down the initial conditions
- Initial volume (V1) = 300 ml
- Initial temperature (T1) = 300 K

### Step 2: Write down the final conditions
- Final temperature (T2) = 276 K
- Final volume (V2) = ?

### Step 3: Use the formula for constant pressure
Since the pressure is constant, we can use the relationship:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
\[ \frac{300 \, \text{ml}}{300 \, \text{K}} = \frac{V2}{276 \, \text{K}} \]

### Step 5: Cross-multiply to solve for V2
Cross-multiplying gives:
\[ V2 = \frac{300 \, \text{ml} \times 276 \, \text{K}}{300 \, \text{K}} \]

### Step 6: Simplify the equation
The 300 K in the numerator and denominator cancels out:
\[ V2 = 276 \, \text{ml} \]

### Step 7: State the final answer
The final volume (V2) of the gas when cooled to 276 K at constant pressure is **276 ml**.

---