Question

The molecules of a given mass of a gas have a rms velocity of 200m/ at 27°C and 1.0 × 105Nm–2 pressure when the temperature is 127°C and pressure is 0.5 × 105 Nm–2, the rms velocity in m/ will be

(A) 100√2

(B) [(100√2)/3]

(C) [(400)/√3]

(D) of these

Answer 1

The correct option (C) [(400)/√3]

Explanation:

Vrms = √(3RT/Mo)

Vrms ∝ √T (1)

Vrms1 = 200 m/*, T1 = 27°C = 300 K

P1 = 1 × 105 N/m2

T2 = 127°c = 400 K

P2 = 0.5 × 105 N/m2

RMS velocity doesn't depend on pressure it depends on temperature only. from (1)

{(Vrms1)/(Vrms2)} = √(T1/T2)

= √(300/400)

= (√3/2)

∴ Vrms2 = (2/√3) × 200 = [(400)/√3]