HW3Solv3 - Homework #3 Solutions Question 1a) Let us start...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Homework #3 Solutions Question 1a) Let us start by calculating the entropy using the given mul- tiplicity function ( N,U ) = log[ g ( N,U )] = 3 N 2 log( U ) + log( C ) The fundamental temperature is defined by 1 = parenleftbigg U parenrightbigg N = 3 N 2 U (1) where we have used the fact that the derivative of log( U ) equals 1/U. We can solve this equation for U to get U = 3 N 2 = 3 Nk B T 2 1b) Take the second derivative of the entropy parenleftbigg 2 U 2 parenrightbigg N = U parenleftbigg 3 N 2 U parenrightbigg N = 3 N 2 U 2 < This tells us that the entropy versus energy curve is concave down, suggesting that the temperature of the system (inverse slope of vs. U ) will increase, with increasing U . Question 2) Let us start by following the hint. The energy is related to the spin excess by U = B M = 2 smB . Using this relation we can write the entropy as a function of energy as ( U ) = U 2 2 m 2 B 2 N , with = log[ g ( N, 0)]. Next use the relation between entropy and temperature given by the first equality in equation ( ?? ) above to get 1 = U m 2 B 2 N In order to get the magnetization, recall that U is related to it by U = MB (considering only the component of magnetic field along magnetization).(considering only the component of magnetic field along magnetization)....
View Full Document

Page1 / 4

HW3Solv3 - Homework #3 Solutions Question 1a) Let us start...

This preview shows document pages 1 - 2. Sign up to view the full document.

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