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Question

At what temperature will the speed of sound in a monoatomic gas be the same as in a diatomic gas at 127C? Molar mass of diatomic and monoatomic gases are in the ratio 16:1.

A
21C
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B
252 K
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C
252C
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D
300C
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Solution

The correct option is C 252C
We know that,
γ of monoatomic gas (γm)=53
γ for diatomic gas (γd)=75

From this, γdγm=2125

Let
vm= velocity of sound in monoatomic gas
vd= velocity of sound in diatomic gas

From the data given in the question,

Speed of sound in monotatomic gas =Speed of sound in diatomic gas.

(i.e) vm=vd

γmRTmMm=γdRTdMd

TmTd=MmMd×γdγm
Tm=(MmMd×γdγm)Td

Given that, MdMm=161

Td=127 C=127+273=400 K

So,
Tm=[116×2125]×400=21 K

Tm=21 K or 252C

Thus, option (c) is the correct answer.

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