Question

Question 4: There is a system consisting of three particles where a particle can be in 0, ?, 3? and 5? energy states. Write the partition functions of the particles that meet the following conditions.

a) If the particles are distinguishable

b) Particles comply with Bose-Enistein statistics

c) If the particles match Fermi-Dirac statistics

Answer #1

Consider a two-particle system. Each particle can have energy 0
and Δ. Compute the partition function for the following case:
a. When particles are distinguishable.
b. When particles are fermions.
c. When particles are Bosons.

Consider a system of distinguishable particles with five states
with energies 0, ε, ε, ε, and 2ε (degeneracy of the states has to
be determined from the given energy levels). Consider ε = 1 eV (see
table for personalized parameters) and particles are in equilibrium
at temperature T such that kT =0.5 eV: (i) Find the degeneracy of
the energy levels and partition function of the system. (iii) What
is the energy (in eV) of N = 100 (see table)...

A
system, at temperature T, has particles that can be in three
different states: s=-1, 0, 1. The energy of the particle is given
by: E_s = -μ*B*s , where μ is a constant and B is an applied
magnetic field.
(a) Find the expected energy value for a system of 3
particles.
(b) Generalize part (a) for a system of N particles

a system of two indistinguishable particles following dirac
statistic, any particles can be at any three quantum level ( E1=0E
, E2=1E , E3=2E ).
calculate the Clustering function at T=0 and T= ∞ .
calculate the average energy .

Consider a system of 2 particles and 4 non-degenerate energy
levels with energies 0, E0, 2E0, 3E0, and 4E0. Taking into account
the various ways the particles can fill those energy states, draw
schemes of all the possible configurations with total energy E =
4E0 for the following cases:
(a) The two particles are distinguishable.
(b) The two particles are indistinguishable bosons.
(c) The two particles are indistinguishable fermions.

Consider a system consisting of three particles:
m1 = 4 kg, 1 =
< 11, -6, 12 > m/s
m2 = 2 kg, 2 =
< -13, 7, -4 > m/s
m3 = 3 kg, 3 =
< -29, 34, 19 > m/s
(a) What is the total momentum of this system?
tot = ______ kg · m/s
(b) What is the velocity of the center of mass of this
system?
cm = ______ m/s
(c) What is the total...

1. Consider a system of 6 particles that can be distributed
among Energy levels labelled 0 through 8. (a) Tabulate the average
number of particles in each level for each of the three cases:
Classical particles, Bosons and Fermions.
(b) Represent the information in your table on a single graph
[you must use different symbols or line types for the 3 cases.
Excel/ Sigma Plot /Mathematica etc. are encouraged, but neat hand-
made graphs are also acceptable]. [You may consult...

Assume you have a system that can have one of six distinct
energy states E1 E2 E3 E4 E5 E6 what is the entropy of an ensemble
of five systems where one system is in energy state E2 three
systems are in energy state E3 and one system is in energy state
E6.
Choose the correct answer
S= Kb ln(120)
S= Kb ln(24)
S= Kb ln(20)
S= Kb ln(5)
S= Kb ln(2)
S=0

1.Can ice cream be money? Answer the question
considering the three functions we discussed.
2. What does it mean “fiat money” and why the modern
economies moved to this payments system?
3. What are the small denomination time deposits? Why
are they in M2 and not in M1?
4. Calculate the deposit multiplier in the case of a
reserve requirement of 15 percent.
5. What is the relation between the reserve requirement
and the deposit multiplier? Discuss and provide one...

Question 4. [20 marks] A jet aircraft employs a system for
monitoring the speed S , pressure P , and temperature T
values of its engines using sensors that operate as follows:
S sensor output = 0 only when T SS (rpm) P sensor output = 0 only
when T PP (psi) T sensor output = 0 only when T TT (℉). Assume
that a HIGH at output W activates the...

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