The atmosphere in our physics lecture room is composed primarily of nitrogen N2

Question

The atmosphere in our physics lecture room is composed primarily of nitrogen N2 (78%) and oxygen O2. On an average day, the temperature of our room is around 19.9 oC. 1) What is average speed (rms) of the nitrogen molecules? vrms = m/sec 2) What is the average speed (rms) of the oxygen molecules? vrms = m/sec 3) Now lets assume we turn the heat up a bit and the air temperature doubles to 39.8 oC. Now what is the average speed (rms) of the nitrogen molecules? vrms = m/sec 4) Now what is the average speed (rms) of the oxygen molecules? vrms = m/sec

Explanation / Answer

v(rms) = sqrt(3*R*T/M) R = 8.314 J/mol/K T = 273+20.6 K = 293.6 K 1) molar mass of nitrogen N2 is M = 28.0g/mol = 0.028kg/mol v(rms) = 511 m/s 2) molar mass of oxygen O2 is M = 32.0g/mol = 0.032kg/mol v(rms) = 478 m/s T = 273 + 41.2 K = 314.2 K 3) molar mass of nitrogen N2 is M = 28.0g/mol = 0.028kg/mol v(rms) = 529 m/s 4) molar mass of oxygen O2 is M = 32.0g/mol = 0.032kg/mol v(rms) = 495 m/s 5) speed of sound in air at 20 C is v = 343 m/s

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