Statistical Mechanics Solutions: R K Pathria Book

In summary, the conversation is about a person asking for resources to find solutions to the end of chapter problems in the book "Statistical Mechanics" by R K Pathria. They mention finding a solution for exercise 1.1 and 2.1, and provide a link to a PDF file. Another person responds by suggesting an expansion method and providing a solution for the first part of the exercise. They also mention that the book may want the solution in the general case, not just for the ideal gas scenario. The conversation ends with a thank you from the original poster.
  • #1
rgshankar76
12
0
I wish to know about web sites or other resourses from where i can get solutions for all the end of the chapter problems for the book on statistical Mechanics by R K Pathria
 
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  • #2
there is' t...

:(
 
  • #3
Why not post the problems here? Most statistical mechanics textbook problems are trivial...
 
  • #4
i 'm coursing statistical mechanics and i need to do all of the excersices of pathria ...

i have do some of then , chapter 1,2 now.. .. but i can't understand the 1.1 and the 2.1

http://img228.imageshack.us/img228/3023/dibujojd7.png [Broken]



well ...i found some kind of solution but i don't know it's really good ... www.mtholyoke.edu/~mktrias/physics/pathria_1.1.pdf[/URL]


i hope any help ... thanks
 
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  • #5
In the last line of the PDF file, you got the expression proportional to:

W(x) = [x(E-x)]^M

with M = 3N/2 and x = E1

You should then proceed, not by saying: "this is a binomial distribution etc. etc." but by expanding around the maximum. The maximum is at x = E/2. Let's put x = E/2 + y, and call

W(x) = W(E/2 + y) = P(y)

and expand:

Log[P(y)] = M [Log(E/2 + y) + Log(E/2 - y)] =

M[2 Log(E/2) + Log(1 + 2y/E) + Log(1 - 2y/E)] =

Let's expand in powers of 2y/E


M [2 Log(E/2) - 4 y^2/E^2 + ...]

So, for small y we have:

P(y) = const. Exp(-4 y^2/E^2)

If you are careful and keep the constant terms, the Gaussian should automatically be correctly normalized.
 
  • #6
ok .. thanks a lot.


and if you know any of the exercise 2.1 let me know...

thans .
 
  • #7
Hi dukemaster !

I don't write english well, my language is spanish... but that's not important here, the important is the physic. The page that you checked isn't bad, but Margaret Trias solved the problem for the ideal gas case. I think that the book want the solution in the general case. I'll tell you the solution of the fisrt part, you can do the last part knowing the first.

Supose that the microestates number is function of E1 and E2 like: O(E1,E2) , where O is Omega (in spanish). The logarithm Ln(O(E1,E2)) decreases more quickly than the fuction O(E1,E2), then, we'll take an expansion in Taylor series about [E1] (averge value), this is:

Ln(O(E1,E2)) =Ln(O([E1],E2))+(E1-[E1])(d_1)Ln(O([E1],E2))+))+(E1-[E1])^2(d_2)Ln(O([E1],E2))+...

where (d_1) is the first derivate with respect E1 and (d_2) the second derivate with respect the same.

Check that the first term in the expansion is constant, the secod is zero (that's the equilibrium condition) and the third is differente to zero, then:

Ln(O(E1,E2)) =C+(E1-[E1])^2 (d_2)Ln(O([E1],E))

taking the exponetial in both sides:

O(E1,E2)) =Aexp{(E1-[E1])^2 (d_2)Ln(O([E1],E))}

that's is the Gaussian in the parameter E1. If you take the case of ideal classical gas O(E)=cte E^(3N/2), you'll find the solution of b).

Greetings to all!

I hope it will serve my comment.
 
  • #8
thanks ALBERTO666 !

o como decimos en chile " Muchas Gracias" jejeje .. I'm Chilean and my english is't too good jeje ...

i saw your answer and i repeat ... thanks.

to do this excercises i need to expand my mind .. and thing more than usual..jeje. well ... Bye
 

What is Statistical Mechanics?

Statistical Mechanics is a branch of physics that uses statistical methods to explain the behavior of a large number of particles, such as atoms or molecules, in a system. It helps to understand and predict the properties of macroscopic systems using the laws of thermodynamics and probability theory.

What is the R K Pathria Book about?

The R K Pathria book, "Statistical Mechanics Solutions," is a comprehensive textbook that provides solutions to the problems presented in Pathria's main textbook, "Statistical Mechanics." It offers a detailed and step-by-step explanation of the solutions to help students understand the concepts and principles of statistical mechanics.

Who can benefit from studying this book?

This book is primarily aimed at students and researchers in the fields of physics, chemistry, and engineering who are interested in learning about statistical mechanics and its applications. It can also be useful for anyone interested in understanding the behavior of complex systems, such as gases, liquids, and solids, at a microscopic level.

What topics are covered in this book?

The book covers a wide range of topics, including the fundamentals of statistical mechanics, classical and quantum statistics, phase transitions, and the kinetic theory of gases. It also delves into more advanced topics such as the Ising model, the theory of critical phenomena, and the Monte Carlo method.

Why is this book important?

Statistical mechanics is a crucial tool for understanding the behavior of matter at a microscopic level. This book provides a comprehensive and in-depth explanation of the principles and applications of statistical mechanics, making it an essential resource for students and researchers in various fields of science and engineering.

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