Thermal Flashcards
Probability of a state
Partition β
β = 1 / (kT)
Partition function
Expectation value of energy (full formula)
Expectation value of energy (partition shortcut)
Entropy in terms of multiplicity
S = k lnΩ
Entropy, given probability of microstates
Shortcut entropy expression for monotomic ideal gas
Classical limit of the partition function
Binomial coefficient
Sterling’s formula
1st law of thermal
ΔU = Q - W
2nd law of thermal
Work in a reversible process
δW = P dV
Differential form of entropy change of a system undergoing a reversible process
δQ = T dS
Integral form of entropy change of a system undergoing a reversible process
Fundamental thermodynamic identity
dU = TdS - PdV
Temperature given by the fundamental thermodynamic identity
Pressure given the fundamental thermodynamic identity
Energy Maxwell relation
Heat capacity at constant volume
Heat capacity at constant pressure
Differentiation of the fundamental thermodynamic identity with respect to T
Difference of heat capacities of an ideal gas
CP - CV = Nk
Change in temperature
Q = mcΔT
Heat engine efficiency
Maximum efficiency of a heat engine
Internal energy of a classical ideal gas
vrms
Speed of sound in an ideal gas, given pressure and density
Speed of sound in an ideal gas, given temperature and mass
Fermi-Dirac distribution
Bose-Einstein distrubtion
Average number of fermions/bosons
Approximation of average number of fermions/bosons if energy levels are spaced closely together
γ
(f+2) / f
Monotomic molecule degrees of freedom
3 translational, f=3
Diatomic molecule degrees of freedom
3 translational, 2 rotational, 2 vibrational, f = 5 +2b
b=0 at room temperature
b=1 at high temperatures
Polyatomic molecule degrees of freedom
3 translational, 3 rotational, 2N vibrational, f=6+2N
N=number of atoms
Solid degrees of freedom
3 vibrational in each kinetic and potential energy
f=6
