Suggestions
Use up and down arrows to review and enter to select.Please wait while we process your payment
If you don't see it, please check your spam folder. Sometimes it can end up there.
If you don't see it, please check your spam folder. Sometimes it can end up there.
Please wait while we process your payment
By signing up you agree to our terms and privacy policy.
Don’t have an account? Subscribe now
Create Your Account
Sign up for your FREE 7-day trial
Already have an account? Log in
Your Email
Choose Your Plan
Individual
Group Discount
Save over 50% with a SparkNotes PLUS Annual Plan!
Purchasing SparkNotes PLUS for a group?
Get Annual Plans at a discount when you buy 2 or more!
Price
$24.99 $18.74 /subscription + tax
Subtotal $37.48 + tax
Save 25% on 2-49 accounts
Save 30% on 50-99 accounts
Want 100 or more? Contact us for a customized plan.
Your Plan
Payment Details
Payment Summary
SparkNotes Plus
You'll be billed after your free trial ends.
7-Day Free Trial
Not Applicable
Renews October 8, 2023 October 1, 2023
Discounts (applied to next billing)
DUE NOW
US $0.00
SNPLUSROCKS20 | 20% Discount
This is not a valid promo code.
Discount Code (one code per order)
SparkNotes PLUS Annual Plan - Group Discount
Qty: 00
SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.
Choose Your Plan
For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!
You’ve successfully purchased a group discount. Your group members can use the joining link below to redeem their group membership. You'll also receive an email with the link.
Members will be prompted to log in or create an account to redeem their group membership.
Thanks for creating a SparkNotes account! Continue to start your free trial.
Please wait while we process your payment
Your PLUS subscription has expired
Please wait while we process your payment
Please wait while we process your payment
A Bose gas is a gas consisting of bosons.
A boson is a particle with integer spin.
The classical regime is that in which gases behave classically, namely
without demonstrating bosonic or fermionic character. We can define the
regime as f 1 or n
nQ.
Term used for a gas when it is too dense to be considered as being in the classical regime, i.e. n > nQ.
The distribution function, f, gives the average number of particles in an orbital.
Also known as bose condensation, the effect of boson crowding in the ground orbital.
The temperature below which Einstein Condensation significantly occurs,
given by τâÉá
.
A classical shortcut that assigns to one particle energy of
τ per degree of freedom in the classical
expression of its energy.
The Fermi energy is defined as the chemical potential at
a temperature of zero: μ(τ = 0) =
.
A Fermi gas is a gas consisting of fermions.
A fermion is a particle with half-integer spin.
The heat capacity of a gas is a measure of how much heat the gas can
hold. We define the heat capacity at constant volume to be:
CVâÉá.
We define the heat capacity at constant pressure to be:
CpâÉá.
A gas of particles that do not interact with each other and are in the classical regime.
The quantum concentration marks the concentration transition between the
classical and quantum regimes, and is defined as
nQ = .
The classical distribution function |
f (
![]() ![]() ![]() |
The chemical potential of an ideal gas |
μ = τ log
![]() ![]() ![]() |
The free energy of an ideal gas |
F = Nτ
![]() ![]() ![]() ![]() ![]() |
The pressure of an ideal gas is given by the ideal gas law |
p =
![]() |
The entropy of an ideal gas |
σ = N
![]() ![]() ![]() ![]() ![]() ![]() |
The energy of an ideal gas |
U =
![]() |
The heat capacities for an ideal gas |
CV =
![]()
Cp =
![]() |
The Fermi-Dirac Distribution function |
f (
![]() ![]() |
The Fermi energy of a degenerate Fermi gas |
![]() ![]() |
The energy of the ground state of a Fermi gas |
Ugs =
![]() ![]() |
The Bose-Einstein Distribution Function |
f (
![]() ![]() |
Please wait while we process your payment