If at STP, velocity of sound in a gas (γ=1.5) is 600 m / s, the r.m.s. velocity of the gas molecules at STP will be

Question

If at STP, velocity of sound in a gas (&gamma;=1.5) is 600 m / s, the r.m.s. velocity of the gas molecules at STP will be (A) 400 m / s (B) 600 m / s (C) 600 √2 m / s (D) 300 √2 m / s

Tardigrade Admin · Accepted Answer

Velocity of sound =√(&gamma; R T/M) RMS speed =√(3 R T/M) (vs/rr m s)=√(&gamma;/3) (vs/r rms )=√(1/2) v mms =600 √2 m / s

Q. If at STP, velocity of sound in a gas $(γ = 1.5)$ is $600 m / s$ , the r.m.s. velocity of the gas molecules at STP will be

$400 m / s$

$600 m / s$

$6002 m / s$

$3002 m / s$

Velocity of sound $= \frac{γ RT}{M}$
RMS speed $= \frac{3 RT}{M}$
$\frac{v _{s}}{r _{r m s}} = \frac{γ}{3}$
$\frac{v _{s}}{r _{r m s}} = \frac{1}{2}$
$v_{mm s} = 6002 m / s$

Q. If at STP, velocity of sound in a gas (γ=1.5) is 600m/s, the r.m.s. velocity of the gas molecules at STP will be

400m/s

600m/s

6002​m/s

3002​m/s