Question

The speed of sound propagation in water at a temperature of 293 K is 1482 m / s. At what helium gas temperature would the speed of sound in it have the same speed of 1482 m / s? Helium gas taken as a monoatomic gas with an adiabatic exponent y = 1.67 and an atomic mass of 4.003 u. Take the universal gas constant from the corresponding tables. (Answer: T = 634 K)

Answer 1

The speed of sound in helium can be expressed as

$$c=\sqrt{\frac{\gamma kT}{m}},\\\space\\ T=\frac{c^2m}{\gamma k}=\frac{1482^2(4.003·1.66·10^{-27})}{1.67·1.38·10^{-23}}=633\text{ K}.$$