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: Theory Check
RMS speed $v_{rms} \propto \sqrt{T}$ (where $T$ is in Kelvin).
Step 2: Analyze Option B
$T_1 = -73^\circ\text{C} = 200\text{ K}$
$T_2 = 527^\circ\text{C} = 800\text{ K}$
$\frac{v_2}{v_1} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$. (Correct)
Step 3: Analyze others
$PV = \frac{2}{3}K.E.$ so (A) and (D) are false. In (C), $T_2/T_1 = 900/173 \neq 16$.
Step 4: Conclusion
Statement (B) is mathematically accurate.
Final Answer:(B)