MCP 1 Chapter 2 Statistical Mechanics
Questions about the lecture 'From Molecular to Continuum Physics 1' of the RWTH Aachen Chapter 2 Statistical Mechanics
Questions about the lecture 'From Molecular to Continuum Physics 1' of the RWTH Aachen Chapter 2 Statistical Mechanics
Set of flashcards Details
| Flashcards | 49 |
|---|---|
| Language | English |
| Category | Computer Science |
| Level | University |
| Created / Updated | 18.02.2017 / 20.02.2017 |
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What is the definition of eps^T? [3]
1. eps^T = n²h²/8ma² with n speed a length
2. peta = h²/8ma² // For n=1
3. eps_n^T = (n²-1)*peta
What is the definition of q^T? [3]
1. q^T = Sum_n exp(-\beta*(n²-1)*peta)
2. q^T = sqrt(2pi*mkT/h²)*a = a/Delta // For 1D container
3. q^T = q_x^T + q_y^T + q_z^T = V/Delta³ with V=abc
What is the definition of eps^R?
eps_J^R = hcB*J(J+1)
What is the definition of q^R for hetero- and homonuclear diatomic? [2]
1. q^R ~ T/sigma*Theta^R with Theta^R = hcB/k
2. sigma is symmetry number // If T>>Theta^R
What is the definition of q^R for nonlinear? [2]
1. q^R ~ pi^1/2*T^3/2 / sqrt(sigma*Theta^A*Theta^B*Theta^C)
2. Theta^X = h²/8pi²*X*k
What holds for nonlinear regarding q^R? [2]
1. Three moments of inertia
2. Three rotational constants
What is the definition of eps^V for 1D harmonic oscillators?
eps^V = (u+1/2)hV
What is the definition of eps^V for coupled harmonic oscillators (So-called polyatomic molecules)? [3]
1. eps^V = Sum_i^f (u_i+1/2)hV_i with degrees of freedom f
2. f = 3N-6 for nonlinear molecule
3. f = 3N-5 for linear molecule
What is the definition of q^V for 1D harmonic oscillators? [2]
1. q^V = exp(-Theta^V/2T)/ 1-exp(-Theta^V/T)
2. Theta^V=hv/k
What is the definition of q^V for coupled harmonic oscillators (So-called polyatomic molecules)?
q^V = T/Theta^V // If T>>Theta^V
What is the definition of q^E?
q^E ~ g_0 * exp(-\beta*eps_0^E) with g_0 = g^E // If >>T
What are the characteristics of the Sackur-Tetrode equation? [4]
1. For monoatomic gas with indistinguishable independent molecules Q=q^N/N!
2. S = [U(T)-U(0)]/T + nR*(ln q – ln N + 1) with N=n*N_A and k=R/N_A
3. Only mode of motion is translation
4. S(T) = nR*ln(e^5/2*V/nN_A*Delta³)
What is the general definition of mean energy <eps^M>?
<eps^M> = - 1/q^M * (dq^M/d\beta)_V with M:=T R V or E
What is the definition of the translation mean energy <eps^T>?
<eps^T> = 3/2 *kT
What is the definition of the rotational mean energy <eps^R>?
<eps^R> = kT
What is statistical mechanics?
Motion of mas objects with mass m under force
What describes statistical mechanics?
Relationship of mis matter behavior and its mas properties
What does statistical mechanics connects?
Thermodynamics to mis behavior (Statistical thermodynamics)
What is statistical mechanics interested in?
Average motion of particles due to number in e.g. one mole
What happens if objects become sufficiently small?
Covered by quantum mechanics?
What are the characteristics of the ensemble concept? [4]
1. Mas observables
2. Collection of systems with mis interactions and mas properties
3. Every system changes due to mis laws of motion from its initial condition to its own unique mis state
4. All systems share at least one extensive property
What are the characteristics of mas observables? [3]
1. Not sensitive to precise mis details
2. Averages A (so-called equilibrium ensembles)
3. Connected to a mis function
What holds for the mas observables connected with a mis function? [3]
1. A=A(r^N,q^N) with coordinates r and momenta q
2. Probability density p=p(r^N,q^N)
3. <A>ens = int int dr^N dq^N A(r^N,q^N)*p(r^N,q^N)
What is the ergodic hypothesis concerning mas observables? [3]
1. Time average equals ensemble average over long times
2. <A>ens = <A>time for t→inf
3. Study via molecular dynamics simulation
What are the characteristics of population p_i concerning mas observables? [2]
1. <A>=Sum_i Ai*pi with population p_i
2. p_i = n_i/N = e^(-\beta*eps_i)/q
What are the characteristics of partition q concerning mas observables? [5]
1. q = Sum_i e^(-\beta*eps_i)
2. q = 1/(1-e^(-\beta*eps)) for equally energy levels
3. q = Sum_l g_l*e^(-\beta*eps_l) for degeneracy g_l
4. lim_T→0 q = g_0 // One surviving term
5. lim_T→inf q = number of molecular states
Which types of ensemble exist? [4]
1. Micro-canonical (N,V,E) 2. canonical (N,V,T) 3. grand-canonical and 4. isobaric-isothermal (N,P,T)
What are the characteristics of a micro-canonical ensemble? [3]
1. Fix energy
2. Fix composition
3. Equal probability for each possible state
What are the characteristics of a canonical ensemble? [4]
1. Varying energy
2. Fix composition
3. Thermal equilibrium with temperature T
4. Probability depends on energy
What are the characteristics of a grand-canonical ensemble? [5]
1. Varying energy
2. Varying composition
3. Thermal equilibrium with temperature T
4. Chemical equilibrium with chemical potentials
5. Probability depends on energy and composition
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