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Question

Calculate the ratio of the speed of sound in neon to that in water vapour at any given temperature.
[molecular weight of neon =2.02×102 kg/mol and of water vapour =1.8×102 kg/mol. Given that water vapour is triatomic]

A
1.023
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B
1.5
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C
1.055
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D
1.8
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Solution

The correct option is C 1.055
Given that,
Molecular weight of the neon, MNe=2.02×102 kg/mol
Molecular weight of the water vapour, MW=1.8×102 kg/mol

The velocity of sound in a medium is given by
v=Eρ=γPρ=γRTM

Let the velocity of sound in neon be vNe and water be vW.
In terms of temperature and molecular weight,
vNevW=γNeMNe×MWγW [as TNe=TW]
Now, as neon is monoatomic i.e (γ=5/3) while water vapour is triatomic i.e (γ=4/3), so
vNevW= (5/3)×1.8×102(4/3)×2.02×102=54×1.82.02=1.055

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