Question
A gas at 300 K has rms speed 500 m/s. If the temperature is doubled and the molar mass is halved (mixture changed), find the new rms speed.
Solution — Step by Step
So .
We have and . So the ratio is .
Final answer:
Why This Works
The rms speed depends on the average kinetic energy per molecule (). Doubling doubles the kinetic energy, which would multiply by . Halving the mass at fixed kinetic energy multiplies by another . Combined: factor of 2.
This “ratio method” saves you from plugging actual values of , , — which is exactly what JEE wants you to skip in 90 seconds.
Alternative Method
Plug numbers brute force using . You’d need to find first from the original data, then recompute. Slow and error-prone in an exam.
Common Mistake
Students confuse rms speed with mean speed and most probable speed. All three scale the same way with and , but their numerical values differ:
Read the question carefully — if it says “average speed”, use , not .
For mixture problems, “molar mass halved” usually means the gas changed from () to something around (). If the question gives specific gases, identify them first — easier than tracking ratios.