254 Thermodynamics and Statistical Mechanics Air is approximately 80% N, and 20%

Question

254 Thermodynamics and Statistical Mechanics Air is approximately 80% N, and 20% (a) Estimate the average molecular weight of air. 15.2 2. Estimate the root-mean-square speed vms of air molecules at 30 15.3 (a) Starting with the velocity ofsound vs.-wp/p, where M/Visma sdet (b) Find a simple expression for the ratio vms/V,nd of the root-mean- 15.4 Use the law of Dulong and Petit to estimate the specific heats of aluminum sity, show that ndkgT/m to the speed of sound. Calculate its value for air. copper, and lead in units of kcal kg K-1. Compare with the experimental valuesit Table 1.2. (The difference between cp and cy can be neglected.)

Explanation / Answer

RMS velocity of gas = sqrt(3RT/m) T = 303.15K

For O2, m = 0.0319 Kg/mol

RMS velocity of O2 = 478.64 m/s

For N2, m = 0.028 Kg/mol

RMS velocity of N2 = 511.027 m/s

Air --> 80% N2 and 20% O2

So, RMS velocity of Air = 0.8*V(N2) + 0.2*V(O2) = 504.55 m/s

Velocity of sound = sqrt (1.4*1.38*303.15/0.02878) (0.02878 = m(O2)0.2 + m(N2)0.8)

= 343.29 m/s

Ratio = 504.55/343.29 = 1.469

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