P2213_HW02_solns_Fall2008 - Physics 2213 HW #2 Solutions...

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- 1 - Physics 2213 HW #2 — Solutions Fall 2008 18.30 [Mixed Gases] a) All gases in the mixture are at the same temperature. The average kinetic energy of a molecule in a gas depends only on the temperature, not on the molecule’s mass, so the average kinetic energy is the same for the molecules of each element. b) Equation (18.19) shows that for constant temperature, the rms speed is proportional to the inverse square root of the mass, and so rms Kr rms Rn rms Ne rms Ne 20.18 20.18 0.491, 0.301 and 83.80 222.00 v v v v = = = = rms Rn rms Kr 83.80 0.614. 222.00 v v = = 18.37 [Oxygen Molecules] a) . J 10 6.21 K) K)(300 J 10 381 . 1 )( 2 3 ( 21 23 - - × = × = kT K 2 3 ave = b) 21 5 2 2 ave ave 3 23 2 2(6.21 10 J) 2.34 10 m s . (32.0 10 kg mol) (6.023 10 molecules mol) 2 K (v ) m - - × = = = × × × c) s, m 2 3 10 84 . 4 mol) kg 10 (32.0 K) K)(300 mol J 3(8.3145 3 × = × = = - M RT v rms which is of course the square root of the result of part (b). d) s) m 2 23 3 10 84 . 4 ( mol) molecules 10 (6.023 mol) kg 10 (32.0 × × × = = - rms A rms v N M mv = 2.57 × 10 - 23 kg m s This may also be obtained from mol) molecules 10 (6.023 mol) kg 10 J)(32.0 10 2(6.21 2 23 3 21 × × × = = - - ave mK p rms e) The average force is the change in momentum of the atom, divided by the time between collisions. The magnitude of the momentum change is twice the result of part (d) (assuming an elastic collision), and the time between collisions is twice the length of a side of the cube, divided by the speed. Numerically, 2 21 19 rms rms ave ave rms 2 2 2(6.21 10 J) 1.24 10 N. 2 (0.100m) mv mv K F L v L L - - × = = = = = × f) 2 17 ave ave 1.24 10 Pa. p F L - = = × g) ( 29 ( 29 5 17 21 ave 1.013 10 Pa 1.24 10 Pa 8.15 10 molecules. p p - = × × = × h) A A N RT pV N n N = = = 1.00 atm ( 29 1.00 L
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This note was uploaded on 10/25/2008 for the course PHYS 2213 taught by Professor Perelstein,m during the Fall '07 term at Cornell University (Engineering School).

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P2213_HW02_solns_Fall2008 - Physics 2213 HW #2 Solutions...

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