Quiz 2

Question 1

P of rolling one 6 after 3 die rolls

Answer 1

1-(5/6)^3

Question 2

P of two successive faces on die rolls

Answer 2

1/36

Question 3

Microstate

Answer 3

Specify the state of each part of the system

Question 4

Macrostate

Answer 4

Give # of particles in each state. Key point: this is an observable

Question 5

Multiplicity

Answer 5

of macrostates compatible with a given microstate

Question 6

P of a microstate

Answer 6

1/(total multiplicity)

Question 7

P of a macrostate

Answer 7

(multiplicity)/(total multiplicity)

Question 8

How many ways to arrange N distinguishable objects?

Answer 8

N!

Question 9

How many ways to draw n objects from N distinguishable objects?

Answer 9

N choose n

Question 10

How many ways to arrange cards in a deck of 52?

Answer 10

52!

Question 11

How many possible strings are there from flipping a coin 10 times?

Answer 11

2^10

Question 12

How many ways to draw 5 cards from a deck of 52 if order doesn’t matter?

Answer 12

52 choose 5

Question 13

How many ways to draw 5 cards from a deck of 52 if order DOES matter?

Answer 13

52!/47!

Question 14

What is the probability of a microstate of a paramagnet system with N magnets?

Answer 14

1/2^N

Question 15

What is the probability of a macrostate with N_up spin up magnets out of N magnets?

Answer 15

(N choose N_up) (1/2^N)

Question 16

What is the probability that a 25 spin magnet system observed every second will have 1 spin up in a year

Answer 16

1-P_never happens^# of seconds in a year

= 1 - ((2^25 - 1)/(2^25))^# of seconds in a year

Question 17

What is Dulong and Petit’s rule? What is the tangible prediction associated with this?

Answer 17

For kB T&raquo_space; hf for an Einstein solid, U = 3N kB T. We can find dU/dT from this rule for various metals; experiments confirm the prediction.

Question 18

How do we define a microstate in the Einstein solid?

Answer 18

A particular configuration of the distribution of energy quanta in each oscillator. We must specify the number of energy quanta that every oscillator has.

Question 19

What is a macrostate for an Einstein solid?

Answer 19

The total energy q

Question 20

What is the multiplicity of an Einstein solid with N oscillators and q energy units?

Answer 20

(q + N - 1) choose q

Question 21

How does the multiplicity of an Einstein solid depend on q?

Answer 21

It goes up (like, with q!)

Question 22

What does it mean for two systems to be weakly coupled?

Answer 22

Energy exchange between elements of one system is very fast compared to energy exchange between the two systems.

Question 23

What is a real world example of two weakly coupled systems

Answer 23

The air inside a house vs the air outside of a house (say, during winter where the heat is running)

Question 24

What is the energy of a quantum harmonic oscillator?

Answer 24

hf(n+1/2)

Question 25

What is a microstate of two weakly coupled systems?

Answer 25

Specification of the energy level of every oscillator in both systems

Question 26

What is a macrostate of two weakly coupled systems? (it’s assumed that we know q_tot)

Answer 26

qA, the energy of one of the systems A and B

Question 27

What is the multiplicity of A where A and B are weakly coupled systems?

Answer 27

multiplicity of A = (qA + N_A - 1) choose qA

Question 28

What is the multiplicity of a particular macrostate qA of the weakly coupled systems A and B?

Answer 28

multiplicity of sys = multiplicity of A * multiplicity of B

Question 29

What is the total multiplicity of weakly coupled systems A and B with q_tot and N_tot?

Answer 29

(q_tot + N_tot - 1) choose q_tot

Question 30

What is the probability of a particular macrostate qA of the weakly coupled systems A and B?

Answer 30

multiplicity of sys / total multiplicity = multiplicity of A * multiplicity of B / total multiplicity