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  4. If at NTP velocity of sound in a gas is 1150 m / s, then the rms velocity of gas molecules at NTP is (Given: R=8.3 J / mol K, Cp=4.8 cal / mol K )

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Q. If at NTP velocity of sound in a gas is $1150\, m / s$, then the rms velocity of gas molecules at NTP is (Given : $R=8.3\, J / mol\, K,\, C_{p}=4.8\, cal / mol\, K$ )

AMUAMU 2006

Solution:

$R=\frac{8.3}{4.2} cal\, g / mol K$
$C_{V} =C_{p}-R$
$=\left(4.8-\frac{8.3}{4.2}\right)=2.824$
$\gamma =\frac{C_{p}}{C_{V}}=\frac{4.8}{2.824}=1.69$
Since, $v=\sqrt{\left(\frac{3}{\gamma}\right)} \times v_{s}$
$=\sqrt{\frac{3}{1.69}} \times 1150$
$=1532.19\, m / s$