Explanation Given Info: A tabulated integral is given as ∫ 0 ∞ x n e − α x d x = n ! α n + 1 where n is a positive integer and α is a positive constant. The expression for f ( v ) is, f ( v ) = 4 π ( m 2 π k T ) 3 2 v 2 e − m v 2 2 k T f ( v ) is the probability per unit speed interval(distribution function). m is mass v is molecular speed. k is Boltzmann constant. T is absolute temperature. Substitute 4 π ( m 2 π k T ) 3 2 v 2 e − m v 2 2 k T for f ( v ) in ∫ 0 ∞ v f ( v ) d v . ∫ 0 ∞ v f ( v ) d v = ∫ 0 ∞ v [ 4 π ( m 2 π k T ) 3 2 v 2 e − m v 2 2 k T ] d v = ∫ 0 ∞ 4 π ( m 2 π k T ) 3 2 v 3 e − m v 2 2 k T d v = 4 π ( m 2 π k T ) 3 2 ∫ 0 ∞ v 3 e − m v 2 2 k T d v Thus, ∫ 0 ∞ v f ( v ) d v = 4 π ( m 2 π k T ) 3 2 ∫ 0 ∞ v 3 e − m v 2 2 k T d v (I) Substitute v 2 for x

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

14th Edition

ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell establishe…

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Chapter 18, Problem 18.78P

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The ∫0∞v f(v)dv integral and compare it to vav .

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Chapter 18, Problem 18.77P

Chapter 18, Problem 18.79P

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Chapter 18 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

Ch. 18.1 - Rank the following ideal gases in order from...Ch. 18.2 - Prob. 18.2TYU Ch. 18.3 - Rank the following gases in order from (a) highest...Ch. 18.4 - A cylinder with a fixed volume contains hydrogen...Ch. 18.5 - A quantity of gas containing N molecules has a...Ch. 18.6 - The average atmospheric pressure on Mars is 6.0 ...Ch. 18 - Section 18.1 states that ordinarily, pressure,...Ch. 18 - In the ideal-gas equation, could an equivalent...Ch. 18 - When a car is driven some distance, the air...Ch. 18 - The coolant in an automobile radiator is kept at a...

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The ∫ 0 ∞ v f ( v ) d v integral and compare it to v a v .

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The ∫0∞v f(v)dv integral and compare it to vav .

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Chapter 18 Solutions