# Thermal Physics, Kittel Chapter 2 problem 2

• kde2520
In summary, the conversation is about finding the equilibrium value of fractional magnetization in a system of N spins in a magnetic field, using the entropy as the logarithm of the multiplicity function. The equilibrium occurs when the entropy is maximized, and the derivative is taken with respect to U to find the value of <s>. The final answer concludes that <s> = 0, indicating that temperature does not affect the spin direction.
kde2520
I'm just reposting this question that someone else asked a long time ago but got no responses. Any help would be great.

Hi,
Studying for my thermal physics final and want to make sure I'm doing this right as our book doesn't have answers. Pretty simple question so I need to make sure I'm doing the basics right.

Find the equilibrium value at temperature $$\tau$$ of the fractional magnetization

$$\frac{M}{Nm} = \frac{2<s>}{N}$$

of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. Take the ntropy as the logarithm of the multiplicty g(N,S) where

$${\sigma}(s) \approx {\sigma}_o - \frac{2s^2}{N}$$

where $${\sigma}_o = \ln{g(N,0)}$$ and g is the multiplicity function. Using the fact that U = 2smB, we can say

$${\sigma}(U) = {\sigma}_o - \frac{U^2}{2m^2B^2N}$$

Now, the equilibrium of the system will occur when the entropy is maximized, so I take the derivative with respect the U, set it equal to zero, solve for U and then use that to find s. This gives me that <s> = 0 which makes sense as the temperature isn't going to affect whether you have spin up or spin down, right?

--------------------------------------------------------------------------------

The fractional magnetization should definitely be non-zero with a non-zero external magnetic field. I haven't solved that problem in a while, but there should definitely be a net magnetization.

## 1. What is thermal physics?

Thermal physics is a branch of physics that studies the behavior of matter at the microscopic level, focusing on the relationship between temperature, energy, and heat transfer.

## 2. What does Kittel Chapter 2 problem 2 cover?

Kittel Chapter 2 problem 2 is about the thermodynamic properties of ideal gases, specifically the relationship between pressure, volume, and temperature known as the Ideal Gas Law.

## 3. What is the Ideal Gas Law?

The Ideal Gas Law is a fundamental equation in thermal physics that describes the behavior of ideal gases. It states that the product of pressure and volume is directly proportional to the temperature and the number of moles of gas, represented by the equation PV = nRT.

## 4. What are some real-life applications of thermal physics?

Thermal physics has many practical applications, including refrigeration and air conditioning systems, engines and turbines, and thermometers. It is also used in industries such as manufacturing, energy production, and materials science.

## 5. How is thermal physics related to other branches of physics?

Thermal physics is closely related to other branches of physics, such as thermodynamics, statistical mechanics, and quantum mechanics. It also has connections to other fields, including chemistry, engineering, and astronomy, as thermal processes are present in all systems and phenomena.

Replies
7
Views
2K
Replies
1
Views
908
Replies
5
Views
2K
Replies
10
Views
2K
Replies
5
Views
1K
Replies
2
Views
1K
Replies
1
Views
3K
Replies
1
Views
3K