Question

Hydrogen gas is filled in two identical bottles, A and B, at the same temperature. The mass of hydrogen in the two bottles is 12 gm and 48 gm respectively. In which bottle will sound travel faster? How may times as fast as the other? (Ans: In A; Twice). Solve the example.

Answer 1

Answer:

Speed of sound in B = 2(Speed of sound in A)

Explanation:

We know that the speed of sound is given by $a = \sqrt{n\gamma RT}$

Where R=gas constant, T= temperature ,n= No. of moles and $\gamma$ is the ratio of specic heat constant.

For A = No.of moles = $\dfrac{12}{1} =12$

For B =  No.of moles = $\dfrac{48}{1} =48$

Speed of sound for A = $\sqrt{12\gamma RT}$

Speed of sound for B = $\sqrt{48\gamma RT}$

$\dfrac{Speed\ of\ sound\ for\ A}{Speed\ of\ sound\ for\ B} = \dfrac{\sqrt{12\gamma RT} }{\sqrt{48\gamma RT} }$ =  $\dfrac{\sqrt{12} }{\sqrt{48} } = \dfrac{1}{2}$

                                                                                         

So, Speed of sound in B = 2(Speed of sound in A)