Answer to Question #88455 in Molecular Physics | Thermodynamics for gc

Question

What is the speed of sound (in m/s) in air at the normal boiling temperature of water?

Answer 1

Speed of sound

$$c = \sqrt{\gamma \frac{p}\rho} =\sqrt{\frac{\gamma RT}M}$$

R (approximately 8.314,5 J · mol⁻¹ · K⁻¹) is the molar gas constant;

γ (gamma) is the adiabatic index. the value is 7/5 = 1.4 for diatomic molecules (as air mainly consist of nitrogen and oxygen)

M is the molar mass of the gas. The mean molar mass for dry air is about 29 g/mol

T is the absolute temperature. normal boiling temperature of water is $T = 373 \, \text{K}$

$$c = \sqrt{\frac{1.4 \cdot8.314 \cdot 373}{0.029}} \, \text{m/s} = 387 \, \text{m/s}$$