Question

To increase the RMS speed of gas molecules by 25%, the percentage increase in absolute temperature of the gas is to be

• A. 42.75
• B. 56.25
• C. 36.75
• D. 18.25

Hint:

Since RMS speed depends on the square root of temperature, square the speed ratio to find temperature ratio, then convert to percentage increase.

Answer 1

The Correct Option is B

The RMS speed \(v_{rms}\) is related to absolute temperature \(T\) by: \[ v_{rms} \propto \sqrt{T} \] Given increase in RMS speed is 25%, \[ \frac{v'_{rms}}{v_{rms}} = 1.25 = \sqrt{\frac{T'}{T}} \Rightarrow \frac{T'}{T} = (1.25)^2 = 1.5625 \] Percentage increase in temperature: \[ (1.5625 - 1) \times 100 = 56.25% \]