Question

Let speed of sound waves in hydrogen gas at room temperature is v_(0). What will be the speed of sound waves in a room which contains an equimolar mixture of hydrogen and 'He' at same temperature :-

Answer 1

Answer:

Speed of the sound in mixture of the gas is given as

$v = \frac{v_0}{\sqrt{1.4}}$

Explanation:

Speed of sound in gas is given as

$v = \sqrt{\frac{\gamma RT}{M}}$

as we know that hydrogen is diatomic gas so we have

$v_0 = \sqrt{\frac{(7/5)RT}{2}}$

Now when equimolar mixture of He and H2 is used then average molar mass is given as

$M = \frac{2 + 4}{2} = 3 g/mol$

now adiabatic constant of the mixture is given as

$\gamma_{mix} = \frac{1(7/2)R + (5/2)R}{(5/2)R + (3/2)R}$

$\gamma_{mix} = \frac{3}{2}$

Now we have

$v = \sqrt{\frac{(3/2)RT}{3}}$

now we have

$\frac{v_0}{v} = \frac{\sqrt{7/10}}{\sqrt{1/2}}$

$\frac{v_0}{v} = \sqrt{1.4}$

$v = \frac{v_0}{\sqrt{1.4}}$

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Topic : Speed of sound

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