Quiz 2 Flashcards
P of rolling one 6 after 3 die rolls
1-(5/6)^3
P of two successive faces on die rolls
1/36
Microstate
Specify the state of each part of the system
Macrostate
Give # of particles in each state. Key point: this is an observable
Multiplicity
of macrostates compatible with a given microstate
P of a microstate
1/(total multiplicity)
P of a macrostate
(multiplicity)/(total multiplicity)
How many ways to arrange N distinguishable objects?
N!
How many ways to draw n objects from N distinguishable objects?
N choose n
How many ways to arrange cards in a deck of 52?
52!
How many possible strings are there from flipping a coin 10 times?
2^10
How many ways to draw 5 cards from a deck of 52 if order doesn’t matter?
52 choose 5
How many ways to draw 5 cards from a deck of 52 if order DOES matter?
52!/47!
What is the probability of a microstate of a paramagnet system with N magnets?
1/2^N
What is the probability of a macrostate with N_up spin up magnets out of N magnets?
(N choose N_up) (1/2^N)
What is the probability that a 25 spin magnet system observed every second will have 1 spin up in a year
1-P_never happens^# of seconds in a year
= 1 - ((2^25 - 1)/(2^25))^# of seconds in a year
What is Dulong and Petit’s rule? What is the tangible prediction associated with this?
For kB T»_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.
How do we define a microstate in the Einstein solid?
A particular configuration of the distribution of energy quanta in each oscillator. We must specify the number of energy quanta that every oscillator has.
What is a macrostate for an Einstein solid?
The total energy q
What is the multiplicity of an Einstein solid with N oscillators and q energy units?
(q + N - 1) choose q
How does the multiplicity of an Einstein solid depend on q?
It goes up (like, with q!)
What does it mean for two systems to be weakly coupled?
Energy exchange between elements of one system is very fast compared to energy exchange between the two systems.
What is a real world example of two weakly coupled systems
The air inside a house vs the air outside of a house (say, during winter where the heat is running)
What is the energy of a quantum harmonic oscillator?
hf(n+1/2)
What is a microstate of two weakly coupled systems?
Specification of the energy level of every oscillator in both systems
What is a macrostate of two weakly coupled systems? (it’s assumed that we know q_tot)
qA, the energy of one of the systems A and B
What is the multiplicity of A where A and B are weakly coupled systems?
multiplicity of A = (qA + N_A - 1) choose qA
What is the multiplicity of a particular macrostate qA of the weakly coupled systems A and B?
multiplicity of sys = multiplicity of A * multiplicity of B
What is the total multiplicity of weakly coupled systems A and B with q_tot and N_tot?
(q_tot + N_tot - 1) choose q_tot
What is the probability of a particular macrostate qA of the weakly coupled systems A and B?
multiplicity of sys / total multiplicity = multiplicity of A * multiplicity of B / total multiplicity
