The ratio of speed of sound in nitrogen gas to that of helium gas at 300k is. 1)✓2/7. 2)✓1/7. 3) ✓7 4) ✓6/5?

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Answer 1 · 2018-06-19T07:44:12

I got $\frac{\sqrt{3}}{5}$ $sqrt(3)/5$

Speed of sound in an ideal gas is given by

$v = \sqrt{\frac{γ RT}{M}}$ $"v" = sqrt((gamma"RT")/"M")$

Where

$underline(bb"Type of gas" color(white)(........) bb(gamma)color(white)(..))$
$"Monoatomic" color(white)(000=) 5/3$

$"Diatomic" color(white)(..............) 7/5$

$"Triatomic" color(white)(......!!!!!!) 4/3$

Nitrogen gas molecules are diatomic and that of Helium are monoatomic. So,

$"v"_("N"_2)/"v"_"He" = sqrt(gamma_("N"_2)/gamma_"He" × "M"_"He"/"M"_("N"_2))$

$color(white)("v"_("N"_2)/"v"_"He") = sqrt((7/5)/(5/3) × (4 cancel"g/mol")/(28 cancel"g/mol")$

$color(white)("v"_("N"_2)/"v"_"He") = sqrt(7/5 × 3/5 × 4/28)$

$color(white)("v"_("N"_2)/"v"_"He") = sqrt(cancel(7)/5 × 3/5 × (cancel(4))/(cancel(4) × cancel(7))$

$color(white)("v"_("N"_2)/"v"_"He") = sqrt(3)/5$