If g(N,s) = N!/[(0.5N +s)!(0.5N-s)!] then what does
g(N,s) represent?
G(N,s) gives the multiplicity (i.e. the number of different ways) in which N 2-state items (e.g. binary spins, coins, etc) can have a spin excess of 2s.
If P(s) indicates a probability distribution function, then we can write <f> = ∑f(s)P(s). Why can’t we use g(N,s) as a probability distribution function directly in this relation for some arbitrary function f?
We can’t use g(N,s)
because it isn’t normalized. That is to
say ∑g(N,s) ≠ 1
Quiz #2: 1/27/03
What can you say about g(U1,U2) for two systems in thermal equilibrium?
It is at its maximum
value.
Quiz #3: 1/31/03
Why doesn’t an isolated system of 4 harmonic oscillators ever have a negative (absolute) temperature?
The number of quantum
states available to the system is not bounded, so as you add energy, entropy
continues to increase.
Quiz #4: 2/3/03
If P(es) is the probability of finding a system in a particular state s, write down an expression for U (i.e. <e>).
U = åesP(es)
Quiz #5: 2/11/03
What does the following equation tell you? (i.e. What exactly is <s>?)
<s>
= 1/(exp(hw/t)-1)
This gives the average
number of photons in a mode of frequency w in a system at temperature t.
Quiz #6: 2/14/03
What is the relationship between radiation in a cavity and blackbody radiation?
At any given temperature,
the radiation that escapes from a small hole in a cavity will have the same
spectrum as the energy radiating from a blackbody. Furthermore, the total flux of energy from the hole and the body
(per unit area) will differ only a simple geometrical factor.
Quiz #7: 2/17/03
What is a phonon?
A phonon is the quantum of
energy associated with elastic waves in solid materials.
Quiz #8: 2/21/03
What drives a flow of particles from one system to another?
A gradient in chemical
potential. (or equivalently, the opportunity to increase the overall entropy).
Quiz #9: 2/28/03
Given that Z = S exp [(Nm - es(N))/t], write down an expression for the average squared energy.
< e2 > = S e s(N)2exp [(Nm - es(N))/t] / Z
Quiz #10: 3/03/03
What are the possible values of the fermi-dirac distribution function f(e)?
1 ³ f(e) ³ 0
Quiz #11: 3/7/03
What defines the classical limit of an ideal gas?
The concentration is much
less than the quantum concentration.
Alternatively, the average occupancy of each orbital is much less than
one.
Quiz #12: 3/28/03
What is the definition of the fermi energy?
The energy of the highest
occupied orbital of a fermi gas in its ground state.
Quiz #13: 4/4/03
What is a Bose-Einstein condensate?
Those atoms in a bosonic
gas that are found in the ground state of the system.
Quiz #14: 4/11/03
When a gas expands isothermally, it does work on its surroundings, yet the energy of the gas remains unchanged (U = 3/2 NkbT and T is fixed). How can this be?
Energy enters as heat
from the surroundings.
Quiz #15: 4/14/03
What is a heat engine?
A heat engine is a device
that converts heat to work (i.e. energy transfer in due to a thermal gradient
and energy transfer out mechanically).
What is a refrigerator?
A refrigerator is a device
that uses work to move heat from a cold reservoir to a hot reservoir.
Quiz #16: 4/21/03
Under what experimental conditions is the Gibbs free energy a relevant quantity?
When the system is
maintained at constant pressure.
Quiz #17: 4/25/03
What is an extensive property of a system?
A property whose value
changes if the system is duplicated is extensive.
Quiz #18: 4/30/03
What does the following expression tell us? P(v) = 4p (M/2pt)3/2 v2 exp(-mv2/2t)
This is Maxwell speed
distribution and it gives the probability of finding a molecule (of mass m)
of an ideal gas (at
temperature t)moving with a speed in the interval between v and v + dv.
Quiz #19: 5/2/03
Transport processes are characterized by the relation Flux = coefficient x driving force.
Choose a transport process and give specfic examples of
these 2 terms.
Here are examples:
Heat flow:
energy, thermal conductivity, temperature gradient
Diffusion:
particles, diffusivity, concentration gradient
Momentum transport:
momentum, viscosity, velocity shear
Electrical conductivity: charge, conductivity,
electrical potential