COMEDK Exam 2019 Solved Paper

The velocity of sound in a gas at a fixed temperature is given by
v=√‌

γRT

M

where, γ=(‌

Cp

CV

) is specific heat ratio and M is the molecular mass of the gas.
Let, velocity of sound in hydrogen, v1=√‌

γRT

M1

Velocity of sound in oxygen, v2=√‌

γRT

M2

Let, M1 and M2 be the molecular mass of hydrogen and oxygen respectively n1 and n2 be the moles of hydrogen and oxygen, respectively.
Molecular mass of the mixture,
M‌mix ‌=‌

n1M1+n2M2

n1+n2

According to the question, n1=n2 at given NTP.
M2‌=16M
M‌mix ‌‌=‌

M1+16M1

2

=‌

17M1

2

Velocity of sound in mixture, v‌mix ‌=√‌

γRT

M‌mix ‌

⇒‌‌v‌mix ‌=√‌

2γRT

17M1

∴ The ratio of velocity of sound in mixture to that of hydrogen
‌

v1

v‌mix ‌

‌=‌

√ γRT M1

√‌ γ2RT 17M1

⇒‌‌‌

v‌mix ‌

v1

‌=√‌

2

17