Question

Select the correct statement.

• A. The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
• B. The temperature of gas is \( -73^\circ\text{C} \). When the gas is heated to \( 527^\circ\text{C} \), the r.m.s. speed of the molecules is doubled.
• C. The temperature of gas is \( -100^\circ\text{C} \). When the gas is heated to \( +627^\circ\text{C} \), the r.m.s. speed of the molecules is four times.
• D. The product of pressure and volume of an ideal gas will be equal to half the translational kinetic energy.

Hint:

Always convert Celsius to Kelvin ($T + 273$) before using gas law ratios.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to verify the kinetic theory of gases relations between pressure, volume, temperature, and molecular speed.
Step 2: Detailed Explanation:
Let's check each statement:
(A) and (D): Kinetic energy \( KE = \frac{3}{2} PV \implies PV = \frac{2}{3} KE \). Both (A) and (D) are incorrect.
(B): \( T_1 = -73^\circ\text{C} = 200 \text{ K} \). \( T_2 = 527^\circ\text{C} = 800 \text{ K} \).
r.m.s speed \( v_{\text{rms}} \propto \sqrt{T} \).
Ratio: \( \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2 \). Speed is doubled. This is correct.
(C): \( T_1 = 173 \text{ K} \), \( T_2 = 900 \text{ K} \). Ratio \( \sqrt{900/173} \approx 2.28 \ne 4 \). Incorrect.
Step 3: Final Answer:
Statement (B) is the only correct statement.