Download 1. Discuss the following concepts

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Equipartition theorem wikipedia, lookup

Entropy in thermodynamics and information theory wikipedia, lookup

H-theorem wikipedia, lookup

Heat transfer physics wikipedia, lookup

Extremal principles in non-equilibrium thermodynamics wikipedia, lookup

Conservation of energy wikipedia, lookup

Maximum entropy thermodynamics wikipedia, lookup

Internal energy wikipedia, lookup

Second law of thermodynamics wikipedia, lookup

Transcript
1. Discuss the following concepts (just writing formulas is not enough, use
words)
Enthropic principle
Closed system
Subsystem
Distribution function
Microcanonical distribution function
2. Consider N identical non-interacting 1D harmonic oscillators. The energy levels of the system will be given by:
N
N
ni +
E = h̄ω
2
i=1
(1)
a For N=2, calculate the total number of states that have energies
less then or equal to E = h̄ω(M + N2 ).
b Generalize the previous result for arbitrary N and obtain an expression for ΓN (E).
c Calculate the total number of states, ΔΓ that the system can be
in if the total energy is exactly E = h̄ω(M + N2 ). How is this result
related to Γ(E)
d Calculate entropy, S. What is the temperature T of the state?
d What is the probability that a particular harmonic oscillator is
in the nth excited state?
e Given a subsystem consisting of 2 harmonic oscillators, what is
the probability that this subsystem has total energy, = h̄ω(n + 1)
Hint: In calculating the probabilities, express you result in terms of
temperature and try to obtain an expression which is proportional to
e− kT
1