Why Do We Need to Outline a Proof for \beta=1/(Kb*T) in Stat Mech?

In summary, the conversation discusses outlining a proof to show that beta = 1/(Kb*T) for a gas of fermions. The approach involves putting the system in thermal contact with a system obeying classical statistics and using the zeroth law to establish that they have the same temperature. The issue with this proof is determining if putting the systems in contact will automatically result in the same beta, and if assuming the same beta will guarantee equilibrium. The question also raises the applicability of this proof to a gas of bosons, despite it being specified for fermions only.
  • #1
sachi
75
1
we have to outline a proof to show that beta =1/(Kb*T) for a gas of fermions. we are supposed to put this system in thermal contact with a system obeying classical statistics, so that the two systems have the same beta, invoke the zeroth law to sat that they have the same temperature, and then show that beta=1/(Kb*T) for the classical system. The problem I have with this proof is that how do we know that just because we put the two system in contact they will have the same beta? Or if we assume that they have the same beta, why will they necessarily be in equilibrium? Also, does our proof apply to a gas of bosons as well? I don't see any reason why it shouldn't, but for some reason the question specifies for fermions only. thanks for your help.

Sachi
 
Physics news on Phys.org
  • #2
How have you defined [tex] \beta [/tex]? I need to know where you're coming from to offer specific advice.
 

Related to Why Do We Need to Outline a Proof for \beta=1/(Kb*T) in Stat Mech?

1. What is statistical mechanics proof?

Statistical mechanics proof is a mathematical framework used to understand and predict the behavior of a large number of particles or molecules in a system. It is based on the principles of thermodynamics and probability theory.

2. How does statistical mechanics proof work?

Statistical mechanics proof uses statistical methods to describe the behavior of a system at the microscopic level, taking into account the interactions between particles. It allows us to make predictions about the macroscopic properties of a system based on the properties of its individual particles.

3. What are the assumptions made in statistical mechanics proof?

There are several assumptions made in statistical mechanics proof, including the assumption of a large number of particles, the particles being in thermal equilibrium, and the particles being indistinguishable. These assumptions allow for simplifications in the mathematical calculations.

4. What are some applications of statistical mechanics proof?

Statistical mechanics proof has many applications in various fields, including physics, chemistry, and materials science. It is used to understand and predict the behavior of gases, liquids, and solids, as well as phase transitions, chemical reactions, and thermodynamic properties.

5. Are there any limitations to statistical mechanics proof?

Although statistical mechanics proof is a powerful and widely used tool, it does have some limitations. It may not be accurate for very small systems, and it may not account for certain complex systems. Additionally, it relies on simplifications and assumptions, which may not always accurately reflect real-world systems.

Similar threads

Tricky Problem: Prove range T = null ##\phi## when null T' has dim 1
    • Calculus and Beyond Homework Help
Replies
8
Views
721
Understanding the Differences Between Bose and Classical Gases
    • Introductory Physics Homework Help
Replies
2
Views
855
I Why do the lines m and l coincide in the proof of the parallelogram rule?
    • Linear and Abstract Algebra
Replies
4
Views
857
I Empirical temperature scales using different thermometers
    • Classical Physics
Replies
7
Views
959
A Proof that the thermal interpretation of QM is wrong
    • Quantum Interpretations and Foundations
2
Replies
59
Views
10K
Stat. Mech: energy-temperature relation of a perfect classical gas
    • Advanced Physics Homework Help
Replies
9
Views
3K
Heat capacity of magnetic dipole in magnetic field
    • Electromagnetism
Replies
1
Views
1K
A Why Do We Need Alchemical Methods to Compute Gibbs Energy Changes?
    • Atomic and Condensed Matter
Replies
1
Views
856
I A Bold New Take on Quantum Theory
    • Quantum Interpretations and Foundations
Replies
25
Views
1K
Why do we need the Lagrangian formulation of Mechanics?
    • Mechanics
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top