What is the meaning of the Stirling Approximation and why
is it useful?
This gives an approximate representation of the factorial function, and is much more rapidly calculated for large numbers.
a)
What is the fundamental assumption of Statistical
Mechanics?
b)
What (in words) is the definition of entropy (in
fundamental units)?
a) All accessible (micro)states of a system are equally likely
b) Entropy is defined as the natural log of the number of states available to a system
Which way would energy flow, if a system of spins at a
temperature of 700k were brought into contact with a system of spins at 900k?
Since 700k is hotter
than 900k, energy will flow from the system at 700k into the other one.
Quiz #4: 2/4/02
If P(es) = exp(-es/t) /Σs (exp(-es/t)), write down the expression for the <es>?
<es> = Σs
{es * exp(-es/t) / Σs
(exp(-es/t))}
Quiz #5: 2/8/02
What is the physical significance of the Helmholtz free energy (F ≡U τσ)?
It gives the amount of
useable energy that can be extracted from a system.
Quiz #6: 2/11/02
What does the Planck distribution function ( 1/{exp(hω/τ)-1})
tell us? (i.e. What does it represent, in words?)
The Planck distribution
tells us the average number of photons in a particular mode (i.e. at a
particular frequency).
Quiz #7: 2/15/02
What is the connection between radiation in a cavity and blackbody radiation?
An object that radiates as
a black body will emit radiation of the same spectrum and intensity as a hole
poked in the side of a cavity that is at the same temperature.
Quiz #8: 2/22/02
In what way is chemical potential analogous to temperature?
Temperature differences
drive the flow of energy between two bodies until thermal equilibrium is
established. Chemical potential
differences drive the flow of particles between two bodies until diffusive
equilibrium is established. There are
other analogies that can be drawn, but this is the most direct.
Quiz #9: 3/4/02
What is the range of possible values for the fermi-dirac distribution function f(ε)?
Since f(ε) gives the
average occupancy of a particular orbital for fermions, it can range
from 0 to 1.
Quiz #10: 4/8/02
What is the relation between the chemical potential of a bose gas and the energy spacing of the lowest orbitals of that gas?
As temperature goes to
zero, the chemical potential approaches the ground state energy. At low temperatures, the difference between
the chemical potential and the ground state energy is small compared to the
difference between the first excited state and the ground state energy.
Quiz #11: 4/15/02
a) What does a heat engine do?
b) What does a refrigerator do?
A heat engine converts
heat into work (i.e. does work using the flow of energy between to bodies at
different temperatures). A refrigerator
uses mechanical energy to create a temperature gradient (i.e. move heat from a
cold body to a hot one, or vice versa.)
Quiz #12: 4/26/02
The law of mass action says that the concentration of reactants depends on what one property of the system?
Temperature.
Quiz #13: 4/29/02
Answer either a or b:
a) The
Maxwell velocity distribution is given by the equation D(v) = (M/2πkT)3/2 4πv2 e-(mv2/2kT)
What does it tell us
(i.e. what does it represent)?
D(v)
gives the probability of finding a particle of an ideal gas with a velocity in
the interval dv centered on v.
b) What
is the numerical value of the integral of D(v), evaluated from 0 to ∞?
Since
this is an integral of probabilities over all possibilities, the answer is 1.
Quiz #14: 5/6/02
Consider two vessels at equal pressures, connected by a tube. The pressure is low enough that they can be considered in the Knudsen regime. Under what circumstances will particles move from one vessel to another, and in which direction?
Particles will move if
there is a temperature gradient between the vessels, and will move from the
colder vessel (where n is greater) to the hotter one.