Karteikarten
Statistical physics
Karten in diesem Stapel (57)
- 1Probability of particle configurationP(N) = C(n)/2^(N)
Where P(N) is the probability of that state
C(n) = the possible combinations for that sate
N = total number of states - 2Molecular flux densityJ(0) = (n/6)v(avg)
Where J(0) = molecular flux density
(molecules m^-2 s^-1)
n = density of molecules
v(avg) = average velocity of molecules(m/s) - 3Pressure of an ideal gasp(avg)=F(M)*N/A=(2mv(avg))J(0) =2/3nε(K)
Where p(avg) = average pressure(Pa)
F(M) = Force per molecule(N)
N = number of molecules
A = area(m^2)
m = mass of a molecule(kg)
v(avg) = average velocity(m/s)
J(0) = molecular flux density
(molecules m^-2 s^-1)
n = density of molecules
ε(K) = average kinetic energy - 4Mean free pathl=1/σn
Where l = mean free path
σ = total cross section
n = density of molecules - 5Centre of mass velocityVcm = (m(1)v(1) + m(2)v(2))/(m(1) +m(2))
Where Vcm = velocity of the centre of mass in a collsion
m(1) = mass of particle 1(kg)
v(1) = velocity of particle 1(m/s)
m(2) = mass of particle 1(kg)
v(2) = velocity of particle 1(m/s) - 6Boltzmann lawn = n(0)exp(-mgh/KT)
Where n = particle density
n(o) = initial particle density
m = mass of gas(kg)
h= height of gas(m)
k = boltzmann constant(m^2 kg s^2 k^-1)
T = temperature(k) - 7Ideal gas lawpv = NKT=nrT
Where p = pressure of gas(pa)
v = volume of gas(m^3)
N= number of particles
K = boltzmann constant(m^2 kg s^2 k^-1)
T = temperature(k)
n = number of moles
r = ideal gas constant(j k mol^-1) - 8What is the the random or disordered state?The most probable configuration or the one that can be obtained in the most ways
- 9What are the two ways interacting systems transfer energy?work or heat(Q)
- 10When there are 2 gases at the same temperature what is the relationship between the mean kinetic energy of the centre of mass motions?They are equal
- 11Is the mean kinetic energy a property of the temperature or the gasthe temperature
- 12What is the first theorem of statistical mechanics also known as the equipartition theoremFor every independent direction of motion, the average kinetic energy is 1/2kt
- 13What happens to the density of particles and the potential energy increasesThe density of particles decreases
- 14What is proportional to the probability of finding a particlular combination of molecules at any seperationexp(-ΣV(r(i,j))/Kt)
Where V(r(i,j)) = the potential of the molecules at seperation between position r(i) and r(j)
t = temperature - 15What happens to the probabillity of finding a molecule at any seperation as the temperature increasesYour are more likely to find particles at any seperation rather than just r(0)
- 16Maxwell boltzmann distributionf(p) dp = Ce^(-K.E./kT) dp
Where f(p) = probability of finding a particle
C = (m/2πKT)^1/2
K.E. = kinetic energy(J)
T = temperature - 17EntropyS = k ln(Ω)
Where S = entropy (j/k)
Ω = number of possible quantum states - 18Describe a micro cannocial state-Isolated system
-(V,U,N) are fixed
- A quantum state is accessisble if (V,U,N) are fixed
-Many Quantum states could be accessible, they are degenerate
-Ω = number of degenerate quantum states - 19The number of degenerate quantum states in a micro cannoical systemΩ =exp((S(U(A)^*)/k
* exp(((U(A)-U(A)^*)^2 S'')/2k)
Where Ω = number of degenerate quantum states
S = entropy
U(A)^* = energy of system A at equilibrium
U(A) = total energy of system A
S'' = second derivative of entropy with respect to U(A) - 20What happens to the fluctuations in energy as the number of particles increasesThe fluctuations in energy tends to zero
- 21Change in entropy of system in contact with anotherΔS = ΔS(A) + ΔS(B) =
Cln(T(fA)/T(iA)) + Cln(T(fB)/T(iB))
=Cln(T(fA)*T(fB)/T(iA)*T(iB))
Where ΔS = change in entropy
ΔS(A),ΔS(B) = Change in entropy of system A,B
C = specific heat capacity
T(fA),T(fB) = final temperature of system A,B
T(iA),T(iB) = initial temperature of system A,B - 22Describe a Cannoical system-An isolated system
-V and N are fixed
-U is not fixed - 23Partition function for quantum statesZ = Σ(j) e^(-U(J)/kT)
Where Z = partition function
U(j) = The energy of state j(J)
T = temperature(k) - 24Define the Boltzmann probability distributionThe probability that a stae is occupied
- 25Boltzmann probability distribution equationp(i) = (e^-U(i)/kT)/Z
Where p(i) = boltzmann probability distribuition
U(i) = energy of state i (j)
T = temperature(k) - 26partition function for energy levelsZ = Σ(n) g(n)e^-ε(n)/kT
Where Z = partition function
n= permitted energy level(eigen state)
g(n) = the degeneracy of the n-th level
ε(n) = energy of energy level n(J)
T = temperature(k) - 27Entropy of a cannonical systemS = -kΣ(i) p(i)ln(p(i))
Where s = entropy (j/k)
p(i) = boltzmann probability distribution - 28free energyF = -KTln(Z)
Where F = free energy(j)
T = temperature(k)
Z = partition function - 29Probability of a sate in a micro canonical ensemblep(i) = 1/Ω
Where p(i) = probability of state i
Ω = total number of accessable states - 30Pressure equation from free energydF = -p dV -S dT
P = -(∂F/∂V)(T) = K(∂(T lnZ)/∂V)(T)
Where F = free energy (j)
P = pressure(Pa)
V = volume(m^3)
S = entropy(J/k)
T = temperature(k)
Z = partition function - 31Entropy equation from free energydF = -p dV -S dT
S = -(∂F/∂T)(V) = K(∂(T lnZ)/∂T)(V)
Where F = free energy (j)
P = pressure(Pa)
V = volume(m^3)
S = entropy(J/k)
T = temperature(k)
Z = partition function - 32Heat capacity equation from EntropydF = -p dV -S dT
C(V) = T(∂S/∂T)(V) = -t(∂^2 F/∂T^2)(V)
Where C(V) = heat capacity at constant volume(J/k)
F = free energy (j)
P = pressure(Pa)
V = volume(m^3)
S = entropy(J/k)
T = temperature(k) - 33Average internal energy equation from free energydF = -p dV -S dT
U =TS +F =TK(∂(TlnZ)/∂T)(V)- KTlnZ
= KT^2(∂lnZ/T)(V)
Where U = Average internal energy(j)
F = free energy (j)
P = pressure(Pa)
V = volume(m^3)
S = entropy(J/k)
T = temperature(k)
Z = partition function - 34For the system to be in equilbrium what 2 free energies must be at a minimumTHe gibbs and helmholtz free energy
- 35Describe a Grand cannoical ensembleIsoalted system
Volume(v) is fixed
U and N aren't constant - 36Chemical potentialμ = (∂U(particles)/∂N)(S,V) = G/N
Where μ = chemical potential(j/kg)
U(particles) = energy of particles(j)
N = number of particles
G = gibbs free energy per particle(j)
S = entropy(j/K)
V = volume(m^3) - 37In a chemical reaction what determines the direction of the reaction?The chemical potential
- 38What will happen when the chemical potential in a reaction is greater on one sideThe side that has a lower chemical potential will have more particles
- 39Chemical potential at constant U and Vμ = -T(∂S/∂N)(U,V)
Where μ = chemmical potential(J/kg)
T = temperature(K)
S = entropy(j/k)
U = energy of system(j)
V = volume(m^3) - 40grand partition functionΞ = Σ(j) exp(-(ε(j)-μN(j))/kT)
Where Ξ = grand partition function
ε(j) = energy of level j(j)
μ = chemical potential(j/kg)
N(j) = number of aprticles in level j
T = temperature(k) - 41grand potentialΦ(g) = U(average) - μN(average) -TS=-KTln(Ξ)
Where Φ(g) = grand potential
U(average) = average energy of system(j)
N(average) = average number of particles
μ = chemical potential(j/kg)
T = temperature(k)
S = entropy(j/k)
Ξ = grand partition function - 42probability for a state in a grand cannonical systemp(i) = e^-(ε(i) - μN(i)/kT) /Ξ
Where p(i) = probability of quantum
state i
ε(i) = energy of state i
μ = chemcial potential(j/kg)
N(i) = Number of particles in state i
T = temperature(k)
Ξ = grand partition function - 43Pressure from grand potentialdΦ(g) = -PdV-Ndμ-SdT
P = -(∂Φ(g)/∂V)(T,μ) = (∂(KTln(Ξ)/∂V)(T,μ)
Where Φ(g) = grand potential
P = pressure(Pa)
V = volume(m^3)
N = number of particles
μ = chemical potential(j/kg)
S = entropy(j/k)
T = temperature(k)
Ξ = grand partition function - 44entropy from grand potentialdΦ(g) = -PdV-Ndμ-SdT
S = -(∂Φ(g)/∂T)(V,μ) = (∂(KTln(Ξ)/∂T)(V,μ)
Where Φ(g) = grand potential
S = entropy(j/k)
V = volume(m^3)
N = number of particles
μ = chemical potential(j/kg)
P = pressure(Pa)
T = temperature(k)
Ξ = grand partition function - 45Average number of particlesdΦ(g) = -PdV-Ndμ-SdT
N = -(∂Φ(g)/∂μ)(V,T) = (∂(KTln(Ξ)/∂μ)(V,T)
Where Φ(g) = grand potential
N = number of particles
V = volume(m^3)
μ = chemical potential(j/kg)
S = entropy(j/k)
P = pressure(Pa)
T = temperature(k)
Ξ = grand partition function - 46The number of atoms absorbed at surface sitesn(i) = 1/1+exp((E(i)-μ)/KT)
Where n(i) = number of atoms absorbed
E(i) = energy of atom i(j)
μ = chemical potential(j/kg)
T = temperature(k) - 47What happens when two particles interfere?If α = 0 then the wave functions are the same and the colission is symmetric meaning the particles exchange sides.
If α = π then the wave functions are opposite and the collision is anti-symmetric meaning the particles stay on the same side - 48What is the differences between Bosons and FermionsBoson's wave function stay the same after a collision(symmetric) whilst fermions go to the opposite(anti-Symmetric)
A Boson's spin is an integral number whilst a Fermions is a halfof an integral
Many Bosons can be in the same state whilst for Ferimions the Pauli exclusion principle applies. - 49Energy of state for a BosonE = n(i)ε(i)
Where E = energy of the state(j)
n(i) = number of particles in that state
ε(i) = energy of the particle in thte state(j) - 50Energy of state for a FermionE = n(i)ε(i)
Where E = energy of the state(j)
n(i) = number of particles in that state, can only equal 0 or 1
ε(i) = energy of the particle in thte state(j) - 51What approximation can be made to partition function for Large numbers of particlesZ(N) ≅ Z(1)^N /N!
Where Z(N) is the partition function for N particles
Z(1) = partition function for one particle
N = total number of particles - 52Fermi-Dirac distribution functionn(k) = -(∂Φ(g)/∂μ)(T,V) = (1+ exp(ε(k)-μ/kT))^-1
where n(k) = number of particles in that state
Φ(g) = grand potential
μ = chemical potential
ε(k) = average kinetic energy(j)
T = temperature - 53Bose-Einstein distribution functionf(k) = -(∂Φ(g)(K)/∂μ)(T,V) = (exp(ε(k)-μ/kT)-1)^-1
Where f(K) = occupation number or the number of particles in state k
Φ(g)(K) = grand potential of state k
μ = chemical potential
ε(k) = average kinetic energy
T = temperature(k) - 54Entropy for the Bose-Einstein distributionS(k) = k((1+f(k))ln(1+f(k))-f(k)ln(f(k))
Where S(k) = entropy of state k
f(k) = occupation number - 55name three properties of black body radiationThey are in perfect equilibrium
They are perfect absorbers(no photons are reflected)
They are perfect emitters(no photons are lost inside) - 56Rayleigh-jeans law for black body radiationu(λ) = E(λ)/V = 8πkT/λ^4
Where u(λ) = energy density for a wave of wavelength λ(j/m^3)
E(λ) = energy of a wave with wavelength λ(j)
V = volume of the cubic enclosure(m^3)
T = temperature(k)
λ = wavelength of the wave(m) - 57Planck formula for blackbody radiationu(λ) = E(λ)/V = 8πhc/λ^5 1/(exp(hc/kTλ) -1)
Where u(λ) = energy density for a wave of wavelength λ(j/m^3)
E(λ) = energy of a wave with wavelength λ(j)
V = volume of the cubic enclosure(m^3)
T = temperature(k)
λ = wavelength of the wave(m)
h= planck's constant
c = speed of light
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- Karteikarten am Statistical physics, erstellt von daniel upton am 06/04/2021.
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- daniel upton
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