Question

The root mean square speed of the molecules of a gas is proportional to ______. [T = Absolute temperature of gas]

• A. \( \sqrt{T} \)
• B. \( \frac{1}{\sqrt{T}} \)
• C. \( T \)
• D. \( \frac{1}{T} \)

Hint:

RMS speed depends on \( \sqrt{T} \); use the kinetic theory formula \( v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \).

Answer 1

The Correct Option is A

The RMS speed of gas molecules is given by: \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}}, \] where \( R \) is the gas constant, \( T \) is absolute temperature, and \( M \) is molar mass. Thus, \( v_{\text{rms}} \propto \sqrt{T} \).
Answer: \( \sqrt{T} \).