Question

At what temperature would the velocity of sound in oxygen be the same as that in nitrogen
at 10°C? The densities of oxygen and hydrogen at NTP are in the ratio of 16:14.​

Answer 1

The temperature at which the velocity of sound in oxygen be the same as that in nitrogen at 10°C is 27.5°C

Given that,

Ratio of density of oxygen to nitrogen=M1:M2 = 16:14

Temparature of nitrogen = 10°C

To find temperature at which the velocity of sound in oxygen be the same as that in nitrogen at 10°C.

The velocity of sound in a medium v,

v=$\sqrt{\frac{kRT}{M} }$

          where k is the adiabatic index

                      R is the gas constant

                      T is the absolute temperature of the gas

                      M is the molecular mass of the gas

Velocity of oxygen at T1 temperaturev1 = $\sqrt{\frac{kRT1}{M1} }$

Velocity of nitrogen at T2 temperaturev2= $\sqrt{\frac{kRT2}{M2} }$

v1=v2

Therefore,

$\sqrt{\frac{kRT1}{M1} }= \sqrt{\frac{kRT2}{M2} }$

Which implies,

$\frac{T1}{M1} =\frac{T2}{M2}$

T1=$\frac{T2*M1}{M2}$

T1=$283*\frac{16}{14}$

T1=300.5K =300.5-273= 27.5°C

The temperature at which the velocity of sound in oxygen be the same as that in nitrogen at 10°C is 27.5°C

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