For a system of one mole of two-level (-0.5 eV and 0.5 eV) distinguishable particles, calculate (at T = 20°C): a) The single particle partition function b) The system's partition function
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Physics
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- Problem 1 Consider a molecular two-level system with a twofold degenerate ground state (la- beled “0") and a threefold degenerate level (labeled “1") with an energy (expressed in wavenumbers) 150.0 cm-1 above the ground state. (a) What is the proportion N1/N of molecules in the higher level at T = 400 K? (b) What is the molecular average energy (relative to the ground state and expressed in wavenumbers) when the temperature is T = 400 K? (c) What is the proportion No/N of molecules in the ground state when T → 0K? (d) What is the proportion N1/N of molecules in the higher level when T →?a) What is the single particle partition function of the system b) What is the U the energy at the system. c) Plot the energy as a function of temperature.If the partition function is Z= VT and V=3 m^3, T=280 K, then the Enthalpy * :will be 1238.91 J 216931.566 J O 345.23 J O 415.77 J O
- (c) For a monatomic perfect gas with a non-degenerate electronic ground state show that at room temperature (ɛ) = 3kT/2. State any assumptions that you make.Q. No 02: a) Consider a system of two identical particles occupying any of three energy levels A, B and C having energies E, 2E and 3E, respectively. The level A is doubly degenerate (A1 and A2) and the system is in thermal equilibrium. Find the possible configurations and the corresponding energy in the following cases: (i) the particles obey Fermi statistics; (ii) the particles obey Bose statistics; and (iii) the particles are distinguishable and obey Boltzmann statistics.2) Consider a linear chain of N +1 atoms, each of mass m. with harmonic forces (which might be modelled by N springs of spring constant K) acting between nearest neighbours. Taking the atoms at each end of the chain to be fixed, find the dispersion relation for longitudinal waves on the chain. For the case when N is very large, find the density of states and an expression for the internal energy at temperature T. Evaluate the internal energy explicitly in the high- and low-temperature limits.
- Consider a lower energy level situated 200 cm-1 from the ground state. There are no other energy levels nearby. Determine the fraction of the population found in this level compared to the ground state population at a temperature of 300 K. Also interpret it physically?Given the internal energy U and entropy S of N weakly interacting particles in a closed system with fixed volume V. U = NkgT² (27In 2) U S = Nkg lnz + T (a) Prove the Helmholtz free energy (b) Prove the Pressure of the system is F = -NkBT ln z P = Nk Tln z) ( TWhat is the partition function for the system shown? a. b. C. d. E₁ Eo -Eo/KT + e-E₁/kT 2e-Eo/kT +3e-ElkT 3e¯ e-Eo/2kT + e-E₁/3kT e-2Eo/kT + e-³E₁/KT
- here R jl and nl is a function of x or k ??? i m confusd advance physics questionn5) Find an explicit relation for the chemical potential u of a 2DEG at a finite temperature.a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ- x and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that state B is unoccupied. In other words, show that the Fermi and Dirac distribution, ƒ(E) 1 eß(E-μ) +1 is "symmetric" about the point E = μ. b) Write simplified, approximate expressions for f(E) when value of E is very close to μ. (i) E < µ, (ii) E» µ 2 and (iii) the