11.The ratio of speed of sound in Nitrogen gas to that in helium at 300Kis (assume both gases to be ideal)-----------

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Solution

Speed of sound in a gas is given by .
$V = \sqrt{\frac{γ R T}{M}} V_{H e} = \sqrt{\frac{γ_{H e} R T}{M_{H e}}} a n d V_{N 2} = \sqrt{\frac{γ_{N 2} R T}{M_{N 2}}} [γ_{H e} = \frac{5}{3}] [γ_{N 2} = \frac{7}{5}] T = 300 K, M_{H e} = 4 a n d M_{N 2} = 14 \frac{V_{N 2}}{V_{H e}} = \sqrt{\frac{γ_{N 2} H e}{γ_{H e} N_{2}}} = \sqrt{\frac{5 \times 4 \times 5}{3 \times 7 \times 14}} = \sqrt{\frac{25 \times 2}{3 \times 7 \times 7}} = \sqrt{\frac{50}{147}} (a n s)$

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