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Question

The speed of sound in hydrogen at NTP is 1270ms-1. Then the speed in a mixture of hydrogen and oxygen in the ratio of 4:1 by volume will be:


A

371ms-1

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B

380ms-1

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C

635ms-1

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D

950ms-1

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Solution

The correct option is C

635ms-1


Step 1: Given information

The speed of sound in hydrogen at NTP, VH2=1270ms-1

The ratio of hydrogen and oxygen by volume is 4:1.

Let,

V is the volume of oxygen.

4V is the volume of hydrogen.

d is the density of hydrogen.

D is the density of the mixture of gases.

The total volume of the mixture of hydrogen and oxygen will be:

=V+4V=5V

and,

Density of oxygen =16×d=16d

Step 2: To find

We have to find the speed of the mixture.

Step 3: Calculating the density of the mixture of gases

We know the formula,

m=v×d

Here,

m is the mass.

v is the velocity.

d is the density.

Now,

Volumeofmixture×Densityofmixture=Volumeofhydrogen×Densityofhydrogen+Volumeofoxygen×Densityofoxygen

By substituting the given values, we get

5V×D=4V×d+V×16dV(5D)=V(4d+16d)5D=20dD=20d5D=4d

Step 4: Calculation of the speed of the mixture

We know the speed of sound in the gas:

V=γρd

Because sound speed is inversely related to the square root of density, then

V1d

The ratio of the speed of mixture and hydrogen is:

VmixVH2=dDVmixVH2=d4dVmixVH2=14VmixVH2=12...(1)

By substituting the speed of sound in hydrogen in (1), we get

Vmix1270=12Vmix=12702Vmix=635m/s-1

Therefore, option C is the correct choice.


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