Speed of sound in an ideal gas is given by
#"v" = sqrt((gamma"RT")/"M")#
Where
- #gamma =#Adiabatic constant
- #"R ="# Ideal gas constant
- #"T ="# Absolute Temperature
- #"M ="# Molecular mass of gas
#underline(bb"Type of gas" color(white)(........) bb(gamma)color(white)(..))#
#"Monoatomic" color(white)(000=) 5/3#
#"Diatomic" color(white)(..............) 7/5#
#"Triatomic" color(white)(......!!!!!!) 4/3#
Nitrogen gas molecules are diatomic and that of Helium are monoatomic. So,
#"v"_("N"_2)/"v"_"He" = sqrt(gamma_("N"_2)/gamma_"He" × "M"_"He"/"M"_("N"_2))#
#color(white)("v"_("N"_2)/"v"_"He") = sqrt((7/5)/(5/3) × (4 cancel"g/mol")/(28 cancel"g/mol")#
#color(white)("v"_("N"_2)/"v"_"He") = sqrt(7/5 × 3/5 × 4/28)#
#color(white)("v"_("N"_2)/"v"_"He") = sqrt(cancel(7)/5 × 3/5 × (cancel(4))/(cancel(4) × cancel(7))#
#color(white)("v"_("N"_2)/"v"_"He") = sqrt(3)/5#
