Question

A balloon filled with an air sample occupies 3 L volume at 35 °C. On lowering the temperature to T, the volume decreases to 2.5 L. The temperature T is [Assume P constant]

• A. \( 25.67 \, ^\circ \text{C} \)
• B. \( 29.17 \, ^\circ \text{C} \)
• C. \( -16.33 \, ^\circ \text{C} \)
• D. \( -20.55 \, ^\circ \text{C} \)

Hint:

Always convert Celsius to Kelvin in gas law problems: \( K = °C + 273 \). Charles's Law: \( V_1/T_1 = V_2/T_2 \) at constant pressure.

Answer 1

The Correct Option is C

Concept: For a gas at constant pressure, Charles's Law states that volume is directly proportional to absolute temperature: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] where temperatures must be in Kelvin.

Step 1: Convert initial temperature to Kelvin. \[ T_1 = 35 + 273 = 308 \, \text{K} \]

Step 2: Apply Charles's Law. \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \quad \Rightarrow \quad \frac{3}{308} = \frac{2.5}{T_2} \] \[ T_2 = \frac{2.5 \times 308}{3} = \frac{770}{3} \approx 256.67 \, \text{K} \]

Step 3: Convert back to Celsius. \[ T = 256.67 - 273 = -16.33 \, ^\circ \text{C} \]