Question

A gas is a mixture of two parts by volume of hyprogen and part by volume of nitrogen at STP. If the velocity of sound in hydrogen at 0^(@) C is 1300 m//s . Find the velocity of sound in the gaseous mixure at 27^(@)C.

Answer 1

The velocity of sound in the gaseous mixure at 27°C is :

• Given : Velocity of sound in hydrogen, VH = 1300 m/s

• Let V and 2V be the volume of nitrogen and hyxrogen in the mixture respectively.

• Total volume of mixture = V+2V = 3V 

• Mass of nitrogen in mixture = V×14 = 14V

And mass of hydrogen in mixture = 2V×2 = 4V 

• Hence, total mass of gaseous mixture =14V + 4V= 18V ,

• Density of mixture is given as,

ρ = total mass/total volume= 18V/3V = 6

• Velocity of sound in hydrogen at 0°C,

VH = √γP/ρH  ..... 1

• Velocity of sound in mixture at 0°C,

Vm = √γP/ρ  ...... 2

• Dividing 2 by 1

Vm/VH = √ρH/ρ 

Vm = VH×√ρH/ρ = 1300×√4/6

Vm = 1061.44m/s 

• Velocity of sound at t°C in a mixture is given by ,

Vt = Vo + 0.61t ,

Vo = Vm = 1061.44

• At t=27°C,

V27 = 1061.44 + 0.61×27

• V27= 1077.91 m/s