Average values The average or mean value of

Average values The average or mean value of a function f(s) over a normalized probability distribution P(s): Normalization condition: For the binomial distribution the probability P(N, s) that the half of the spin excess is s: the mean square spin excess The fractional fluctuation of 2 s is characterized by:

Energy of the Binary Magnetic System - Thermal properties of the binary magnetic systems become relevant when elementary magnets are placed in magnetic field - energy of a single magnetic moment m, in external magnetic field (let us assume the magnetic field in the z direction, which is in the direction of the elementary spins) - energy of the whole system of N elementary magnets, each with two allowed orientation in the direction of the external field (M is the total magnetization of the system, and m the magnetic moment of one spin. ) - the value of the energy for moments that interact only with the external magnetic field is completely determined by the value of s ! - difference between adjacent levels in the energy spectrum is:

Problems: Consider the function. Maxwell velocity distribution (this distribution function gives us the probability (P) that in an ideal gas a randomly chosen molecule at one time moment will have a velocity around the value of v, in a unit velocity interval: ) 1. Sketch the graphical form of this distribution function, and show that it is normalized to unity. 1. Calculate <v>. 2. Calculate <v 2>. 3. Calculate the most probable velocity. Extra problem: Staring from the form of the distribution functions [f(vx)], f(vy), f(vz)] for the components of the velocity in the x, y and z direction, in an ideal gas --> derive the Maxwell velocity distribution function (given above)!