I will start to solve several problems on this book starting this coming week. I will like to help by posting the solutions. Can you provide the password so I can post solutions? email me at ude.csu|orravanf#ude.csu|orravanf.

Thanks,

Francisco

thnxs!!!!

Expected value of W:

Variance of W:

If q<1 then

In the problem and therefore we require that ; thus when we have closed sum

On the other hand,

Because

To find required we have

or

Equation (10) has only one solution(this can be shown comparing derivatives of rhs and lhs functions):

To satisfy requirement of we give result in limit form:

QED

1st law:

Enthalpy definition:

Enthalpy differential:

Maxwell equation from (2):

Definition of heat capacity and insertion (1) into definition:

Write entropy as function of T and v:

Derive expression for entropy differential and use (4) and (5):

Insert (7) into (1):

QED

Part 2

van der Waals equation:

Express p:

At constant T equation (8) becomes:

Differentiate (10) at constant v and put into (11):

QED

(the "mathematical equation" button), then use LaTeX to type your equations.

If you are new to LaTeX, you can learn it quickly at [http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/]

Derive the principal thermodynamic connection formulas for this ensemble.

When i try to derive the partition function I am getting a term that makes no sense. I was wondering if anyone could help me?

thanks

I have taken the liberty of adding a link to Statistical Mechanics from the WikiNode page of www.SklogWiki.org. SklogWiki is a Wiki for people interested in thermodynamics, statistical mechanics, and the computer simulation of materials, in particular liquids and soft condensed matter. See About SklogWiki for more details. Users of Statistical Mechanics are, of course, more than welcome tocontribute to SklogWiki.

All the best,
Dr. Carl McBride.

Define the Legendre transform that replaces with and with :

then

Now use to get

We can now write the following Maxwell relation for this fundamental relation:

Now carry out the differentiation on the left hand side:

which the desired result.

P/KT = rho(1) + rho(2) + B20(T)*rho(1)^2 + B11(T)* rho(1)*rho(2) + B02*rho(2)^2 +…………….
rho =density(=N/V)

and find an expression for the coefficients B20(T), B11(T), B02(T).

again show that if the virial expansion is written in the form

P/KT = rho + B2(T)* rho^2+ …………………..

with rho= rho(1) + rho(2) , then

B2(x,T)= (x1^2)*B20(T) + x1*(1-x1) * B11(T) + ((1-x1)^2)* B02(T)

where x1= mole fraction of component 1.

From the thermodynamic potential:

for constant N (number of molecules) we can write:

And from Maxwell Transformation:

By substituting equation (4) into equation (1) we get:

Which is true as:

Copies of the book can be ordered directly from the publisher.

I welcome you to the site and I encourage you to submit solutions. If you have any questions or would like to moderate one or more chapters, please contact me.

Julian Talbot

The most probable value of the molecular speed occurs when the derivative of the function is equal to 0

Solving for v;

The mean v is determined, as shown below, where is utilized

The root-mean-square speed is computed as follows, where is utilized

In the isothermal-isobaric ensemble, the partition function can be written as

From which the average enthalpy can be obtained as

Therefore

where we have used the definitions and

Relations between the two sets of virial coefficients can be determined as follows;

First solve equation 1 for p and substitute into equation 2 as follows;

Collecting terms within equation 3 with common powers of V,

In order to write equation 4 as equation 1, the following must be true,

The low temperature limiting form of the heat capacity according to the Einstein model is as follows;

Make the proper substitutions provided within the question in order to convert Cartesian coordinates to a spherical polar coordinate representation;

Integrate equation 2 over all space with respect to and

For the fraction of molecules with speeds between v and v + dv, substitute p=mv to get

is the same as for a three-dimensional diatomic gas;

with a degeneracy of 2 for all J except J=0, for which the degeneracy is 1;

Since is the same as a three dimensional diatomic gas and the is q(T) becomes

The average energy becomes

Start with:

Using the relationship;

Also,

Rearranging equation 6 and substituting into equation 5 results in

Rearranging equation 7 results in

Substitute equation 8 into equation 1 to get

which is always true

Show for bosons

Using the same methodology as above the following equations are derived

Substituting equation 12 into equation 11 results in

Substituting equation 13 into equation 10 results in

Rearranging equation 14 results in

Which is always true

Substitute giving

This suggests the gamma function. So let or
Substituting gives

Using the definition of the gamma function finally gives

If then

Utilizing Euler's Theorem;

Take the derivative of both sides with respect to ;

Set equal to 1;

Rearrange the equation;

Substitute into equation 1 to get

The terminal velocity is attained when the net force on the body is zero. This gives

To solve the equation of motion we use the result that

Integrating gives

Integrating again gives

For large t, this gives