Question

The root mean square velocity of molecules of gas is

• A. Inversely proportional to square root of temperature $\left(\sqrt{\frac{1}{T}}\right)$
• B. Proportional to square root of temperature $(\sqrt{T})$
• C. Proportional to square of temperature $\left(T^2\right)$
• D. Proportional to temperature (T)

Answer 1

The Correct Option is B

1. The root mean square velocity (\(v_{\text{rms}}\)) is given by: \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}}, \] where \(R\) is the universal gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass.
2. From the formula, \(v_{\text{rms}} \propto \sqrt{T}\).
Thus, the root mean square velocity is proportional to the square root of temperature. The root mean square velocity depends on the square root of the temperature, as higher temperatures lead to higher molecular speeds.