Answered: Consider a collection of N… | bartleby

Related questions

Question

Consider a collection of N non-interacting one-dimensional harmonic oscillators, with total
Hamiltonian
H(p, q) = E +ma²q}]:
2
[2m
(a) Calculate the classical partition function, taking the phase-space element to be
dpdq/t, where t is an arbitrary scale factor.
(b) Obtain the entropy, internal energy, and heat capacity.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

(c) Consider a system of two qubits with canonical basis states {|0) , |1)}. Write down an example for a two- qubit density matrix corresponding to a separable pure state and an example for a two-qubit density matrix corresponding to an entangled pure state.
Consider a classical ideal gas in three dimensions, with N indistin- guishable atoms confined in a box of volume V = L³. Assume the atoms have zero spin and neglect any internal degrees of freedom. Starting from the energy levels of a single atom in a box, find: (a) The Helmholtz free energy F (b) The entropy o (c) The pressure p (d) The chemical potential u (e) If the effect of the gravitational field of the Earth is taken into account (constant gravitational acceleration g), the chemical potential would also depend on the height h from some reference point which can be taken to be the sea level. Find u(h) in this case
Please help to prove this to be true
Consider a classical ideal gas of N diatomic heterogeneous molecules at temperature T. The charac- teristic rotational energy parameter is € = 1 and the natural frequency of vibrations is wo. Consider the temperature region where T≫er/kB, but T is of the order of ħwo/kB. Ignore contributions from all other internal modes. Calculate the canonical partition function, the average energy, and the heat capacity at constant volume, Cv.
Calculate the partition function of a two-level system at 25 °C with an energy gap of 10-2¹ J, assuming: a) Both states are non-degenerate. b) The ground state is non-degenerate, and the excited state is 3-fold degenerate.
A diatomic gas molecule can be in one of two vibrational energy levels, separated by 0.1 eV. Give the probabilities to be in either state and use these to calculate their relative populations at room temperature, T≈ 300 K. [You may use that kB ≈ 8.6 × 10−5 K eV−1]
Needs Complete solution with 100 % accuracy.
Consider a three-dimensional infinite-well modeled as a cube of dimensions L x L x L. The length L is such that the ground state energy of one electron confined to this box is 0.50eV. (a) Write down the four lowest energy states and evaluate their corresponding degeneracy. (b) If 15 (total) electrons are placed in the box, find the Fermi energy of the system. (c) What is the total energy of the 15-electron system? (d) How much energy would be required to lift an electron from Fermi energy of part (b) to the first excited state? Need full detailed answers and explanations to understand the concept.