AverageSpeed

AverageSpeed - Average Molecular Speed ex/kT ni n = (2mkT)...

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Colby College Average Molecular Speed n i n = e ε x /kT (2 π mkT) ½ a/h P( v x ) d v x = m 2 π kT ½ e –m v x 2 /2kT d v x P( v x ) d v x = m 2 π kT ½ e –m v x 2 /2kT d v x = 1 0 0.0005 0.001 0.0015 0.002 0.0025 0 1000 2000 P(c) c (m s -1 ) 298 K 1000 K 2000 K P( v x, v y, v z ) d v x d v y d v z = m 2 π kT 3 / 2 e –m( v x 2 + v y 2 + v z 2 ) /2kT d v x d v y d v z c 2 = v x 2 + v y 2 + v z 2 P(c) d v x d v y d v z = m 2 π kT 3 / 2 e –mc 2 /2kT d v x d v y d v z P(c) dc = m 2 π kT 3 / 2 0 π 0 2 π e –mc 2 /2kT c 2 sin θ dc d θ d φ Maxwell-Boltzmann Distribution of Molecular Speeds P(c) dc = 4 π m 2 π kT 3 / 2 e –mc 2 /2kT c 2 dc c = 0 c P(c) dc c = 4 π m 2 π kT 3 / 2
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