Question

Calculate the temperature at which the velocity of sound in oxygen will be as same as that in hydrogen at 50°C.​

Answer 1

Given: Velocity of sound in Hydrogen at 50°C

To Find: the temperature at which the velocity of sound in oxygen will be as same as that in hydrogen at 50°C

Explanation:

As per Kinetic Molecular Theory of gases, the speed of sound in gas is directly proportional to square root of temperature and inversely proportional to square root of molar mass.

So, $v$∝$\sqrt{\frac{T}{M} }$

Let $v_{1}=$velocity of sound in Hydrogen

$T_{1}$= Temperature of Hydrogen= 50°C= 323 K

$v_{2}$= velocity of sound in oxygen

$T_{2}$=Temperature of Oxygen

$M_{1} =$Molar mass of Hydrogen= 1 u

$M_{2} =$Molar mass of Oxygen= 16 u

$\frac{v_{1} }{v_{2} }= \frac{\sqrt{M_{2}T_{1} }}\sqrt{M_{1}T_{2} }{}$

$\frac{v_{1} }{v_{2} }=\frac{\sqrt{5168 }}{\sqrt{T} }$

We know, $\frac{v_{1} }{v_{2} } =1$

so, $\sqrt{5168}=\sqrt{T}$

Squaring on both sides,

We get: $T=5168$

Temperature of oxygen will be 5168 K or 4895°C