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, Volume 2 - Technology Update Custom Edition for Texas A&M - College Station, 2/e

1st Edition

ISBN: 9781323390382

Author: YOUNG

Publisher: Pearson Education

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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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University Physics, Volume 2 - Technology Update Custom Edition for Texas A&M - College Station, 2/e

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...Ch. 18 - Unwrapped food placed in a freezer experiences...Ch. 18 - A group of students drove from their university...Ch. 18 - The derivation of the ideal-gas equation included...Ch. 18 - A rigid, perfectly insulated container has a...Ch. 18 - (a) Which has more atoms: a kilogram of hydrogen...Ch. 18 - Use the concepts of the kinetic-molecular model to...

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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