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

Option: 1

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


Option: 2

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


Option: 3

\mathrm{\frac{m_{1}}{m_{2}}}


Option: 4

\mathrm{\frac{m_{2}}{m_{1}}}


Answers (1)

best_answer

Speed of sound in a gas is given by

\mathrm{V} =\sqrt{\frac{\gamma R T}{M}}, V \propto \frac{1}{\sqrt{M}}
\mathrm{\therefore \quad \quad \frac{V_{1}}{V_{2}} =\sqrt{\frac{M_{2}}{M_{1}}}=\sqrt{\frac{m_{2}}{m_{1}}}}
\mathrm{Here, \gamma=\frac{C_{P}}{C_{V}}=\frac{5}{3}}  for both the gases \mathrm{\left(\gamma_{\text {monoatomic }}=\frac{5}{3}\right)}

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