# Statistical Physics - average energy of a system.

• Jalo
In summary, the conversation discusses finding the temperature of a system with three particles in contact with a heat reservoir, in which each particle can have an energy of 0 or ε. The question is posed as to what temperature would result in a mean energy of 1.2ε. The conversation explores using the equipartition theorem to find the temperature, but the original poster is uncertain if it is the correct approach without more information. Another person provides a helpful Wikipedia link explaining the relationship between average energy and temperature.
Jalo

## Homework Statement

Imagine a system, in contact with a heat reservoir, with three particles. Each particle may be in a state of energy 0 or ε.

What's the temperature of the reservoir such that the mean energy of the system, <E>, is 1.2ε?

## The Attempt at a Solution

I tried using the formula:

S = Kb ln(Ω(E))
dS/dE = Kb / Ω(E) = 1/T

However I don't think this is the right way to go. Since I only know the average value of the energy I don't think I can find the temperature of the system!

Any hints would be highly appreciated!

Thanks.

## 1. What is the definition of average energy in statistical physics?

The average energy of a system in statistical physics is the sum of the energies of all the particles in the system divided by the total number of particles. It is a measure of the overall energy of the system and is used to describe the behavior of particles in a statistical manner.

## 2. How is average energy related to the temperature of a system?

The average energy of a system is directly proportional to its temperature. As the temperature of a system increases, the average energy of the particles in the system also increases. This is because higher temperatures result in increased molecular motion and thus, higher energy levels.

## 3. What is the significance of calculating the average energy of a system in statistical physics?

Calculating the average energy of a system allows us to understand and predict the behavior of particles in a system. It is a fundamental concept in statistical physics and is used to describe the macroscopic properties of a system based on the microscopic behavior of its particles.

## 4. How is the average energy of a system affected by external factors?

The average energy of a system can be affected by external factors such as pressure, volume, and the number of particles in the system. Changes in these factors can result in changes in the average energy of the system, which in turn can impact the overall behavior of the system.

## 5. Can the average energy of a system ever be equal to zero?

In statistical physics, the average energy of a system can never be equal to zero. This is due to the existence of quantum fluctuations, which ensure that there is always some amount of energy present in a system, even at absolute zero temperature. However, in certain cases, the average energy of the system can approach zero, but it can never reach it completely.

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