Two monoatomic ideal gases 1 and 2 of molecular masses and respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]

Question

Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]

Smart Achievers · Accepted Answer

(2)

$V = \sqrt{\frac{γ R T}{M_{0}}},$ $where M_{0} = molecular mass$

$So, V \propto \sqrt{\frac{1}{M_{0}}} \Rightarrow \frac{V_{1}}{V_{2}} = \sqrt{\frac{M_{02}}{M_{01}}} = \sqrt{\frac{m_{2}}{m_{1}}}$

Solution

Q.
Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]

1 $\sqrt{\frac{m_{1}}{m_{2}}}$

2 $\sqrt{\frac{m_{2}}{m_{1}}}$

3 $\frac{m_{1}}{m_{2}}$

4 $\frac{m_{2}}{m_{1}}$

Ans.
(2)

$V = \sqrt{\frac{γ R T}{M_{0}}},$ $where M_{0} = molecular mass$

$So, V \propto \sqrt{\frac{1}{M_{0}}} \Rightarrow \frac{V_{1}}{V_{2}} = \sqrt{\frac{M_{02}}{M_{01}}} = \sqrt{\frac{m_{2}}{m_{1}}}$

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Solution

Q. Two monoatomic ideal gases 1 and 2 of molecular masses m1 and m2 respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by [2000]

1 m1m2

2 m2m1

3 m1m2

4 m2m1

Ans. (2) V=γRTM0, where M0=molecular mass So, V∝1M0⇒V1V2=M02M01=m2m1