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 1 (Chs. 1-20) (14th Edition)

14th Edition

ISBN: 9780133978049

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

See similar textbooks

Concept explainers

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…

Question

Chapter 18, Problem 18.78P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18, Problem 18.77P

Chapter 18, Problem 18.79P

Students have asked these similar questions

Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume your house is the only one using electric power. At a substation the primary of a step-down transformer (turns ratio = 1:23) receives the voltage from the high-voltage transmission line. Because of your usage, a current of 51.1 mA exists in the primary of the transformer. The secondary is connected to the primary of another step- down transformer (turns ratio = 1:36) somewhere near your house, perhaps up on a telephone pole. The secondary of this transformer delivers a 240-V emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.

In some places, insect "zappers," with their blue lights, are a familiar sight on a summer's night. These devices use a high voltage to electrocute insects. One such device uses an ac voltage of 3970 V, which is obtained from a standard 120-V outlet by means of a transformer. If the primary coil has 27 turns, how many turns are in the secondary coil? hel lp?

Hi, Does Quantum physics theory means all branches for example quantum relativity, Quantum mechanics, Quantum field theory, and string theory? Can you explain each one of them? Best

Chapter 18 Solutions

University Physics with Modern Physics, Volume 1 (Chs. 1-20) (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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

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

Solution Summary: The author explains the value of the integral displaystyleunderset0overset

Concept explainers

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

Want to see the full answer?

Chapter 18 Solutions