If at NTP, velocity of sound in a gas is 1150 m/s, then find out the rms velocity of gas molecules at NTP. (Given R=8.3J/mol/K, `C_(P)=4.8` cal/mol/k).

Options

A. `1600"ms"^(-1)`
B. `1532.19"ms"^(-1)`
C. `160"ms"^(-1)`
D. Zero

Answer

B

Explanation

`R= (8.3)/(4.2)"cal "g"mol"^(-1)-K^(-1)`
`C_(v)=C_(p)-R=(4.8-(8.3)/(4.2))=2.824`
`gamma=(C_(p))/(C_(v))=(4.8)/(2.824)=1.69`
`"Since", " " v=sqrt(((3)/(gamma)))v_(s)=sqrt((3)/(1.69))xx1150=1532.19"ms"^(-1)`