Explanation 1) Concept: We use the concept rms speed, average speed, and speed distribution function to calculate the different quantities. 2) Formulae: i) ∫ P v d v = 1 ii) v a v g = ∫ v P v d v iii) v r m s 2 = ∫ v 2 P v d v iv) N o . o f p a r t i c l e s = N ∫ v 1 v 2 P v d v v) F r a c . o f p a r t i c l e s = ∫ v 1 v 2 P ( v ) d v 3) Given: From the graph, we can find out the speed distribution for different ranges given in the figure. 4) Calculations: a) Value of a v 0 : The distribution function gives the fraction of particles with speeds between v and v + d v , so its integral over all speeds is unity. ∫ P v d v = 1 Evaluate the integral by calculating the area under the curve. The area of the triangular part is half the product of base and height, i.e., a v 0 . So, ∫ P v d v = 1 2 a v 0 + a v 0 ∫ P v d v = 3 2 a v 0 1 = 3 2 a v 0 a v 0 = 2 3 …………………………………………………………1) a v 0 = 0.67 b) Ratio of v a v g / v 0 : The average speed is given by v a v g = ∫ v P v d v For the triangular part of the distribution, P v = a v / v 0 And the involvement of this portion is v a v g = a v 0 ∫ 0 v 0 v 2 d v = a 3 v 0 v 0 3 Substituting the value of a v 0 from equation 1), we get v a v g = 2 9 v 0 For the rectangular part, P v = a , so the contribution of this part is v a v g = ∫ v P ( v ) d v v a v g = a ∫ v 0 2 v 0 v d v v a v g = a 2 ( 4 v 0 2 - v 0 2 ) v a v g = 3 a v 0 2 2 Substituting the value of a = 2 3 v 0 from equation 1) in the above equation, we get v a v g = v 0 Therefore, v a v g = 2 9 v 0 + v 0 v a v g = 11 9 v 0 v a v g = 1

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ISBN: 9781119306856

Author: Halliday

Publisher: WILEY

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Chapter 19, Problem 37P

To determine

To find:

a) Value of av0

b) Ratio vavg/v0

c) Ratio vrms/v0

d) The fraction of particles that has a speed between 1.5v0 and 2.0v0

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Chapter 19, Problem 36P

Chapter 19, Problem 38P

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Chapter 19 Solutions

Fundamentals Of Physics - Volume 1 Only

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a) Value of a v 0 b) Ratio v a v g / v 0 c) Ratio v r m s / v 0 d) The fraction of particles that has a speed between 1.5 v 0 and 2.0 v 0

Solution Summary: The author explains the concept of rms speed, average speed and speed distribution function to calculate the different quantities.

Concept explainers

To find:

a) Value of av0

b) Ratio vavg/v0

c) Ratio vrms/v0

d) The fraction of particles that has a speed between 1.5v0 and 2.0v0

Want to see the full answer?

Chapter 19 Solutions

a) Value of a v 0 b) Ratio v a v g / v 0 c) Ratio v r m s / v 0 d) The fraction of particles that has a speed between 1.5 v 0 and 2.0 v 0

Solution Summary: The author explains the concept of rms speed, average speed and speed distribution function to calculate the different quantities.

Concept explainers

To find: a) Value of av0 b) Ratio vavg/v0 c) Ratio vrms/v0 d) The fraction of particles that has a speed between 1.5v0 and 2.0v0

Want to see the full answer?

Chapter 19 Solutions

To find:

a) Value of av0

b) Ratio vavg/v0

c) Ratio vrms/v0

d) The fraction of particles that has a speed between 1.5v0 and 2.0v0