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The molecules of a given mass of a gas have rms velocity of 200 m s⁻¹ at 27°C and 1.0×10⁵ N m⁻² pressure. When the temperature and pressure of the gas are respectively 127°C and 0.05×10⁵ N m⁻², the rms velocity of its molecules in m s⁻¹ is

Asked in NEET 2016 Phase-I · Speed with temperature and molar mass

• (1) (100√2)/3
• (2) (100)/3
• (3) 100√2
• (4) (400)/(√3)

Step-by-step solution

Why the other options are wrong

• (1) Implies a factor √2/6≈0.24 on the starting speed; the gas has been heated, so its molecules cannot have slowed to a quarter of their speed.
• (2) Implies a factor 1/6. The falling pressure is a red herring: vᵣₘₛ=√3RT/M contains no P at all once the temperature is fixed.
• (3) Is 200/√2 — the temperature ratio put upside down and then mis-taken as a half. Heating from 300 K to 400 K must multiply the speed by √4/3=1.15, not divide it.

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