exam1.Fall09Template

exam1.Fall09Template - s 1 ,s 2 ,...,s N . Here, each...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Name October 2, 2009 Chemistry 120B Hour Examination Useful formulas First law of thermodynamics: dE = dq + dw , where dE stands for differential change in internal energy, dq stands for differential heat flow into system, and dw stands for work done on the system. Entropy, S = k B ln Ω, and reversible heat flow: TdS = dq rev , where k B is Boltzmann’s constant, Ω is the number of microstates at energy E and T = ∂E/∂ Ω is temperature. Probability of j th microstate for a system in equilibrium in the canoncial ensemble at temperature T = ( k B β ) - 1 : P j = e - βE j /Q where E j is the energy of the j th microstate, and Q is the canonical partition function: Q = X j e - βE j Gaussian integral: Z -∞ dxe - αx 2 = r π α Maxwell-Boltzmann velocity distribution: Φ( v ) exp ( - βmv 2 / 2) = exp [ - βm ( v 2 x + v 2 y + v 2 z ) / 2] where m is the particle mass, and v is the magnitude of the vector with Cartesian components v x , v y , and v z . 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Name 1. Consider a magnet at temperature T composed of N non- interacting micromagnets with the microstates specified by the list of all the spin states for the micromagnets:
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s 1 ,s 2 ,...,s N . Here, each micromagnet spin state has one of two values: s i = ± 1 , i = 1 , 2 ,...,N . The net energy of the system in one of these microstates is-h ∑ N i =1 s i , where h is a constant magnetic field. 2 Name 2. For the magnet considered in Problem 1, the reversible work differential for the first law of thermodynamics is dw rev = hdM with M denoting the average net spin, i.e., M = h s 1 + s 2 + ... + s N i . At small enough values of h , the equation of state for the magnet is βh = m , where m = M/N . For the questions that follow, assume the system is in this regime of small h . 3 3. Consider N identical classical particles of mass m in two dimensions, i.e., d = 2. These particles are at equilibrium, in a fixed volume and at a temperature T . 4...
View Full Document

This note was uploaded on 01/03/2011 for the course CHEM 120B taught by Professor Geissler during the Spring '08 term at Berkeley.

Page1 / 4

exam1.Fall09Template - s 1 ,s 2 ,...,s N . Here, each...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online