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

Question #88455
What is the speed of sound (in m/s) in air at the normal boiling temperature of water?
1
Expert's answer
2019-04-29T09:44:19-0400

Speed of sound


c=γpρ=γRTMc = \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=373KT = 373 \, \text{K}


c=1.48.3143730.029m/s=387m/sc = \sqrt{\frac{1.4 \cdot8.314 \cdot 373}{0.029}} \, \text{m/s} = 387 \, \text{m/s}


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