物理(分子運動論)一問

9. (a) rms speed of N2 = square-root[3 x 8.31 x (273+20)/0.014] m/s = 722 m/s
rms speed of O2 = square-root[3 x 8.31 x (273+20)/0.016] m/s = 676 m/s

(b) Air contains 78% N2 and 21% O2. Hence, average speed of air molecules = (722x0.78 + 676x0.21) m/s = 705 m/s

7.Mass of a molecule = 0.028/6.02x10^23 kg = 4.65x10^-26 kg
since, kinetic energy of a molecule = (3/2).(1.38x10^-23).(273+27) J = 6.21x10^-21 J
hence, (1/2).(4.65x10^-26)v^2 = 6.21x10^-21
where v is the rms speed of a molecules
solve for v gives v = 516.8 m/s

1. Apply the ideal gas equation PV = nRT to vessel X
(150x10^3)V = 2R(300)
where V is the volume of the vessel
V = (4x10^-3)R

For vessel Y,
P(4x10^-3R) = 3R(600)
P = 450000 Pa = 450 kPa