Question

The ratio of densities of nitrogen and oxygen is 14:16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at $55{}^{\circ }C$ is

• A. $35{}^{\circ }C$
• B. $48{}^{\circ }C$
• C. $65{}^{\circ }C$
• D. $14{}^{\circ }C$

Answer 1

Answer: (B)

The velocity in a gas is given $c=\sqrt{\frac{3RT}{V_{\rho }}}$ given ${\rho }_{N_2}:{\rho }_{O_2}=14:16$ Hence, $c\propto \sqrt{\frac{T}{\rho }}$ Since, velocity in nitrogen and oxygen is same $\sqrt{\frac{T_{N_2}}{{\rho }_{N_2}}}=\sqrt{\frac{T_{O_2}}{{\rho }_{O_2}}}$ or $T_{N_2}{\rho }_{O_2}=T_{O_2}{\rho }_{N_2}$ $T_{N_2}=\frac{{\rho }_{N_2}}{{\rho }_{O_2}}\times T_{O_2}=\frac{14}{16}\times 55=48.125$ $\approx 48{}^{o}C$