MCQ
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 ........... $m / s$
- A$400$
- B$600$
- ✓$600 \sqrt{2}$
- D$300 \sqrt{2}$
✓
Answer
Correct option: C.
$600 \sqrt{2}$
c
(c)
(c)
Velocity of sound $=\sqrt{\frac{\gamma R T}{M}}$
$RMS$ speed $=\sqrt{\frac{3 R T}{M}}$
$\frac{v_s}{r_{ ms }}=\sqrt{\frac{\gamma}{3}}$
$\frac{v_s}{r_{ ms }}=\sqrt{\frac{1}{2}}$
$v_{ rms }=600 \sqrt{2} \,m / s$
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