A statistical system is composed of N particles with spin , immersed in a magnetic field...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A statistical system is composed of N particles with spin , immersed in a magnetic field H. The particles are fixed in their positions and possess a magnetic moment . The Hamiltonian of such a system is H=-H Oi N i=1 where o = +1 (a) Given that the separation between the spins in the lattice is larger than their de Broglie wavelength, should the spins be treated as distinguishable or indistinguishable particles? (b) Write down the canonical partition function, QN, for the N particles. (c) Determine the total energy for this system at an arbitrary temperature, T. (d) Magnetization is defined as the M = (N+ - N_) where N+ and N are the average number of up and down spins, respectively. Determine M for a given temperature T. The susceptibility is defined as X = = (OH) Find the small magnetic field limit of the susceptibility. A statistical system is composed of N particles with spin , immersed in a magnetic field H. The particles are fixed in their positions and possess a magnetic moment . The Hamiltonian of such a system is H=-H Oi N i=1 where o = +1 (a) Given that the separation between the spins in the lattice is larger than their de Broglie wavelength, should the spins be treated as distinguishable or indistinguishable particles? (b) Write down the canonical partition function, QN, for the N particles. (c) Determine the total energy for this system at an arbitrary temperature, T. (d) Magnetization is defined as the M = (N+ - N_) where N+ and N are the average number of up and down spins, respectively. Determine M for a given temperature T. The susceptibility is defined as X = = (OH) Find the small magnetic field limit of the susceptibility. A statistical system is composed of N particles with spin , immersed in a magnetic field H. The particles are fixed in their positions and possess a magnetic moment . The Hamiltonian of such a system is H=-H Oi N i=1 where o = +1 (a) Given that the separation between the spins in the lattice is larger than their de Broglie wavelength, should the spins be treated as distinguishable or indistinguishable particles? (b) Write down the canonical partition function, QN, for the N particles. (c) Determine the total energy for this system at an arbitrary temperature, T. (d) Magnetization is defined as the M = (N+ - N_) where N+ and N are the average number of up and down spins, respectively. Determine M for a given temperature T. The susceptibility is defined as X = = (OH) Find the small magnetic field limit of the susceptibility.
Expert Answer:
Related Book For
Fundamentals of Thermodynamics
ISBN: 978-0471152323
6th edition
Authors: Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen
Posted Date:
Students also viewed these mathematics questions
-
Gold has served as a medium of exchange and a store of value. The increase in trade led each country to set a par value for its currency in terms of gold. The gold standard as an international...
-
In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...
-
What kind of innovation would an improved electric toothbrush be?
-
Suppose you are looking at the 2006 results of how the Echo generation classified specified items as either luxuries or necessities. Do you expect the results to reflect how the Echo generation would...
-
Solve the given systems of equations by using the inverse of the coefficient matrix. x 3y 2z = 8 (17) 2x + 7y + 3z = 19 x y 3z = 3
-
Consider two alternatives, each of which will accomplish the same EPA-mandated pollution control. Using an incremental IRR analysis, determine the preferred alternative assuming MARR is 20...
-
Pringle Corporation has been authorized to issue 20,000 shares of $100 par value, 7%, noncumulative preferred stock and 1,000,000 shares of no-par common stock . The corporation assigned a $5 stated...
-
An airplane flies level in the + x direction 1 0 0 m above the ground at 1 6 0 m / s . the plane drops goods and supplies to some people on the ground. 1 . Draw the path the supplies would follow...
-
A business sold some inventory that had cost $ 5 , 0 0 0 before taxes. The sale is subject to 5 % goods and services tax ( GST ) and 7 % provincial sales tax ( PST ) . The business uses a perpetual...
-
Jordan Manufacturing installed new lighting in the warehouse last year. The company also saw a 22% profit increase last year. Tia said that the new lighting must have resulted in the profit increase....
-
Ann wants to take out a home equity loan to purchase a second home. Her mortgage debt load will be $400,000 for the first home and $250,000 for the second home ($650,000 total). On what amount may...
-
Emily's state on her death includes below assets: Cottage RRSP ACB $ 410760 $259797 FV $ 736526 $350332 Assuming 55% MTR, calculate the tax her state must pay
-
Scenario : Alexis Earns the average salary for a welder 5-10 years into their career, which is $60,000 Is 28 years old and hasn't started saving for retirement yet. Would like to retire at 67, when...
-
The Financial Accounts of the United States (flow of funds or FoF) is a great source of data to understand the circular flow of economic resources in the financial system. A key shortcoming of these...
-
6-6 Lead melts at 620F and tin melts at 450F. They form a eutectic containing 62 percent tin at 360F. The maximum solid solubility of tin in lead at this temperature is 19 percent; of lead in tin, 3...
-
Suppose that a flow network G = (V, E) violates the assumption that the network contains a path s t for all vertices V. Let u be a vertex for which there is no path s u t. Show that there must...
-
Oxygen gas in a piston cylinder at 300 K, 100 kPa with volume 0.1 m3 is compressed in a reversible adiabatic process to a final temperature of 700 K. Find the final pressure and volume using constant...
-
One kilomole of air (assumed to be 78% nitrogen, 21% oxygen, and 1% argon) at room temperature is heated to 4000 K, 200 kPa. Find the equilibrium composition at this state, assuming that only N2, O2,...
-
An air-water vapor mixture enters a steady flow heater humidifier unit at state 1: 10C, 10% relative humidity, at the rate of 1 m3/s. A second air-vapor stream enters the unit at state 2: 20C, 20%...
-
The perfectly competitive model assumes that firms know when marginal revenue equals marginal costs. a. If a firm doesnt have this information, can it produce at the profit-maximizing level of...
-
Hundreds of music stores have been closing in the face of stagnant demand for CDs because of new competition by online music vendors. a. How would price competition from these new sources cause a...
-
A California biotechnology firm submitted a tomato that will not rot for weeks to the U.S. Food and Drug Administration. It designed such a fruit by changing the genetic structure of the tomato. What...
Study smarter with the SolutionInn App