Physical Chemistry Third Edition

386 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium

Exercise 9.2

For the quiz scores in Exercise 9.1, find the mean of the squares of the scores

〈

w^2

〉



∑M

i 1

piw^2 i

and the square root of the mean of the squares, called theroot-mean-square (rms)value, denoted

bywrms.

PROBLEMS

Section 9.1: Macroscopic and Microscopic States of
Macroscopic Systems

9.1A set of people has the following distribution of annual

income:

Annual income/$ Number of people

33,000 12

34,000 15

35,000 18

36,000 24

37,000 19

38,000 20

39,000 12

40,000 8

55,000 2

95,000 3

a.Find the probability of each income.

b.The median of a set of numbers is defined such that

half of the members of the set are greater than or

equal to the median, and half are less than or equal to

the median. Find the median income of this set of

people.

c.Find the mean income.

d.Find the root-mean-square income.

e.Find the mode.

f.Explain any differences between these average values.

9.2A group of people has the following distribution of annual

income:

Annual income/$ Number of people

32,000 2

34,000 5

36,000 13

38,000 24

40,000 26

42,000 20

44,000 12

50,000 8

65,000 3

95,000 2

a.Find the probability of each income.

b.Find the median income of our set of people.

c.Find the mean income.

d.Find the root-mean-square income.

e.Find the mode.

f.Explain any differences between these average values.

9.2 A Model System to Represent a Dilute Gas

Adilute gasis a gas at a low enough pressure that it obeys the ideal gas law to an

adequate approximation. We now define a model system to represent a dilute gas of a

single monatomic substance:

1. The system consists of a large number,N, of identical particles, each with massm.


2. The particles are vanishingly small in size. We call thempoint-mass particles.