Question

Find the temperature at which the speed of sound in oxygen is equal to that in hydrogen at °C . Oxygen is 16 times denser than hydrogen.

Answer 1

Dear student
$$\begin{gathered} Velocityofsoundininagasis \\ V=\sqrt{\frac{\gamma RT}{M}} \\ Velocityofsoundininaoxygengasis \\ {V}_{o_2}=\sqrt{\frac{\gamma RT}{M_{\left(o_2\right)}}} \\ Velocityofsoundininahydrogengasatt°Cis \\ {V}_{H_2}=\sqrt{\frac{\gamma R(273+t)}{M_{\left(H_2\right)}}} \\ Accordingtoquestion \\ \sqrt{\frac{\gamma RT}{M_{\left(o_2\right)}}}=\sqrt{\frac{\gamma R(273+t)}{M_{\left(H_2\right)}}} \\ \frac{\gamma RT}{M_{\left(o_2\right)}}=\frac{\gamma R(273+t)}{M_{\left(H_2\right)}} \\ \frac{T}{M_{\left(o_2\right)}}=\frac{(273+t)}{M_{\left(H_2\right)}} \\ T=\frac{M_{\left(o_2\right)}}{M_{\left(H_2\right)}}\times (273+t)=16\times (273+t) \\ Ift=0°Cthan \\ T=16\times 273=4368K \\ Regards \end{gathered}$$