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Question 3 i. Explain how from the partition function is possible to obtain the average energy...
question no 4.22, statistical physics by Reif Volume 5 4.92 Mean energy of a harmonic oscillator A harmonic oscillator...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
I. Show how to derive the system's partition function from that of a molecule. What approximation...
I need help with this question?
i. Show how to derive the system's partition function from that of a molecule. What approximations are involved? Given the system's partition function, derive a general expression for its internal energy.
i. Show how to derive the system's partition function from that of a molecule. What approximations are involved? Given the system's partition function, derive a general expression for its internal energy.
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can be approximated as an integral. Remember that the rotational energies as a function of rotational quantum number j are given by: ϵ (j) = B j (j + 1) where B is called the “rotational constant” B = ℏ2 /2µ r 2 , and the degeneracy of each "j" state is D(j) = 2j + 1. B. What is the average rotational energy in...
1. Quick Exercises (a) In lecture 15, we showed that the canonical partition function, Q, is...
1. Quick Exercises (a) In lecture 15, we showed that the canonical partition function, Q, is related to the Helmholz free energy: A = -kTinQ. Using the fundamental thermo- dynamic relation of Helmheltz free energy i.e. dA = -SAT - PDV + pdN), express P, and p in terms of Q. (b) The canonical partition function for N non-interacting, indistinguishable parti- cles in volume V at temperature T is given by Q(N,V,T) = where where q(V.T) is the partition function...
I need help with my Physics II (Non-Calculus) homework. How do I solve for each and...
I need help with my Physics II (Non-Calculus) homework. How do I
solve for each and what would the answers be? Thank you!
0.5 Problems Due January 28, 2019 In order to obtain good marks you solutions must include the following: 1. Identify yourself in order to obtain credit, that is put your name in the upper left hand corner of the page 2. Write legibly - If I have to spend time trying to figure out what you are...
QUESTION 2 a) Define solar thermal energy and explain the working principle of Active water heating...
QUESTION 2 a) Define solar thermal energy and explain the working principle of Active water heating system with neat sketch. (5 marks) b) Explain how hot water is produced in Evacuated Tube Collector (5 marks) c) Explain the working principle of Photo Voltaic cells in generating electrical energy. (5 marks) d) To obtain high amount of solar energy from PV panel, what are the key factors to be considered (5 marks)
Question 7 When the conduction electrons in a metal are treated as an ideal gas of...
Question 7 When the conduction electrons in a metal are treated as an ideal gas of fermions, the mean number of electrons occupying a state with energy e is given by I+ (-2) (3)u (a) Define the Fermi energy [ marks] (b) Sketch n as a function of e for an electron gas: (i) at T 0 K, and to the Fermi temperature (ii) at a temperature above 0 K, but small compared Label and briefly justify each sketch [5...
Question 4: (i) Write down the form of the Bose-Einstein distribution and discuss the phenomenon ...
Question 4: (i) Write down the form of the Bose-Einstein distribution and discuss the phenomenon of Bose-Einstein condensation for a boson gas in three dimensions. In particular, carefully explain why the chemical potential becomes very close to the energy of the lowest single- particle state at sufficiently low temperature and describe how that changes the usual approach of replacing a discrete sum over energies with a continuum integral. Discuss how the occupation of the lowest single-particle state changes as a...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
question no 4.22, statistical physics by Reif Volume 5
4.92 Mean energy of a harmonic oscillator A harmonic oscillator has a mass and spring constant which are such that its classical angular frequency of oscllation is equal to w. In a quantum- mechanical description, such an oscillator is characterized by a set of discrete states having energies En given by The quantum number n which labels these states can here assume all the integral values A particular instance of a...
I need help with this question?
i. Show how to derive the system's partition function from that of a molecule. What approximations are involved? Given the system's partition function, derive a general expression for its internal energy.
i. Show how to derive the system's partition function from that of a molecule. What approximations are involved? Given the system's partition function, derive a general expression for its internal energy.
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
1. Quick Exercises (a) In lecture 15, we showed that the canonical partition function, Q, is related to the Helmholz free energy: A = -kTinQ. Using the fundamental thermo- dynamic relation of Helmheltz free energy i.e. dA = -SAT - PDV + pdN), express P, and p in terms of Q. (b) The canonical partition function for N non-interacting, indistinguishable parti- cles in volume V at temperature T is given by Q(N,V,T) = where where q(V.T) is the partition function...
I need help with my Physics II (Non-Calculus) homework. How do I
solve for each and what would the answers be? Thank you!
0.5 Problems Due January 28, 2019 In order to obtain good marks you solutions must include the following: 1. Identify yourself in order to obtain credit, that is put your name in the upper left hand corner of the page 2. Write legibly - If I have to spend time trying to figure out what you are...
QUESTION 2 a) Define solar thermal energy and explain the working principle of Active water heating system with neat sketch. (5 marks) b) Explain how hot water is produced in Evacuated Tube Collector (5 marks) c) Explain the working principle of Photo Voltaic cells in generating electrical energy. (5 marks) d) To obtain high amount of solar energy from PV panel, what are the key factors to be considered (5 marks)
Question 7 When the conduction electrons in a metal are treated as an ideal gas of fermions, the mean number of electrons occupying a state with energy e is given by I+ (-2) (3)u (a) Define the Fermi energy [ marks] (b) Sketch n as a function of e for an electron gas: (i) at T 0 K, and to the Fermi temperature (ii) at a temperature above 0 K, but small compared Label and briefly justify each sketch [5...
Question 4: (i) Write down the form of the Bose-Einstein distribution and discuss the phenomenon of Bose-Einstein condensation for a boson gas in three dimensions. In particular, carefully explain why the chemical potential becomes very close to the energy of the lowest single- particle state at sufficiently low temperature and describe how that changes the usual approach of replacing a discrete sum over energies with a continuum integral. Discuss how the occupation of the lowest single-particle state changes as a...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
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