Question

An ideal gas is heated from \( 27^\circ\text{C} \) to \( 627^\circ\text{C} \) at constant pressure. If initial volume of gas is \( 4 \text{ m}^3 \), then the final volume of the gas will be

• A. $2 \text{ m}^3$
• B. $4 \text{ m}^3$
• C. $6 \text{ m}^3$
• D. $12 \text{ m}^3$

Hint:

- Always convert temperature to Kelvin - $V \propto T$ at constant pressure

Answer 1

The Correct Option is D

Concept: At constant pressure (Charles' law): \[ \frac{V}{T} = \text{constant} \]

Step 1: Convert temperatures to Kelvin.
\[ T_1 = 27 + 273 = 300\ \text{K} \] \[ T_2 = 627 + 273 = 900\ \text{K} \]

Step 2: Apply Charles' law.
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] \[ \frac{4}{300} = \frac{V_2}{900} \]

Step 3: Solve for $V_2$.
\[ V_2 = \frac{4 \times 900}{300} = 12\ \text{m}^3 \]