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Q.

The speed of sound in hydrogen gas is $v 0$ at temperature $T 0$ . Then the speed of sound in the mixture of helium and oxygen gas having same number of moles at temperature $T 0$ is

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a

v 0 3

b

521 v 0

c

314 v 0

d

542 v 0

answer is C.

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Detailed Solution

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$V = \sqrt{\frac{γ R T}{M}}$

$V_{0} = \sqrt{\frac{7 R T}{5 (2)}}$

$V_{mix} = \sqrt{\frac{γ_{mix} R T}{M_{M i x}}}$

$M_{mix} = \frac{n [4] + n [32]}{2 n} = 18$
$\frac{2 n}{γ_{mix} - 1} = \frac{n}{(\frac{7}{5} - 1)} + \frac{n}{(\frac{5}{3} - 1)}$

$\Rightarrow γ_{m i x} = \frac{3}{2}$

So, $V_{m i x} = \sqrt{\frac{5}{42}} V_{0}$

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The speed of sound in hydrogen gas is v 0 at temperature T 0 . Then the speed of sound in the mixture of helium and oxygen gas having same number of moles at temperature T 0 is