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At which temperature the speed of sound in hydrogen will be same as that speed of sound oxygen at 100\degree C.

  • Option 1)

    -148\degree C

  • Option 2)

    -212.5\degree C

  • Option 3)

    -317.5\degree C

  • Option 4)

    -249.7\degree C

 

Answers (1)

best_answer

Speed of sound in gases is v = \sqrt{\frac{\gamma RT}{M}}\Rightarrow T \alpha M

(Because v, \gamma - constant ) . Hence \frac{T_{_{H_{2}}}}{T_{O_{2}}} = \frac{M_{_{H_{2}}}}{M_{O_{2}}}

\Rightarrow \frac{T_{_{H_{2}}}}{(273 + 100)} = \frac{2}{32} \Rightarrow T_{H_{2}} = 23.2 K = -249.7 ^{o} C

 

Effect of density on speed of sound -

\frac{V_{1}}{V_{2}}= \sqrt{\frac{\gamma _{1}}{\gamma _{2}}\times \frac{\rho _{2}}{\rho _{1}}}

 

- wherein

\gamma _{1}\; and\; \gamma_{2} are ratio of specific heat.

\rho _{1}\; and\; \rho _{2} are densities.

 

 

 


Option 1)

-148\degree C

This is incorrect.

Option 2)

-212.5\degree C

This is incorrect.

Option 3)

-317.5\degree C

This is incorrect.

Option 4)

-249.7\degree C

This is correct.

Posted by

Avinash

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