Question

If the temperature of a gas is increased from 27°C to 927°C, the rms speed is:

• A. gets halved
• B. gets doubled
• C. becomes 4 times
• D. does not change

Hint:

The rms speed of a gas is proportional to the square root of the temperature. If the temperature doubles, the rms speed will increase by a factor of \( \sqrt{2} \).

Answer 1

The Correct Option is B

The rms speed \( v_{\text{rms}} \) is proportional to the square root of the temperature: \[ v_{\text{rms}} \propto \sqrt{T} \] The ratio of rms speeds when the temperature changes from \( T_1 \) to \( T_2 \) is: \[ \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{1200}{300}} = \sqrt{4} = 2 \] Hence, the rms speed gets doubled.