Solution Found!
Consider a two-state paramagnet with 1023 elementary
Chapter 2, Problem 23P(choose chapter or problem)
Problem 23P
Consider a two-state paramagnet with 1023 elementary dipoles, with the total energy fixed at zero so that exactly half the dipoles point up and half point down.
a) How many microstates are “accessible” to this system?
b) Suppose that the microstate of this system changes a billion times per second. How many microstates will it explore in ten billion years (the age of the universe)?
c) Is it correct to say that, if you wait long enough, a system will eventually be found in every “accessible” microstate? Explain your answer, and discuss the meaning of the word “accessible.”
Questions & Answers
QUESTION:
Problem 23P
Consider a two-state paramagnet with 1023 elementary dipoles, with the total energy fixed at zero so that exactly half the dipoles point up and half point down.
a) How many microstates are “accessible” to this system?
b) Suppose that the microstate of this system changes a billion times per second. How many microstates will it explore in ten billion years (the age of the universe)?
c) Is it correct to say that, if you wait long enough, a system will eventually be found in every “accessible” microstate? Explain your answer, and discuss the meaning of the word “accessible.”
ANSWER:
Solution to 23P
Step 1
(a)
We need to find the number of microstates accessible to the system of a two-state paramagnet with 1023. elementary dipoles,with half dipoles pointing up and half pointing down.
N=1023
Taking log at both the sides,
Thus the number of microstates is very large for N=1023