Derivation of sackur-tetrode equation

  • Thread starter Thread starter ralden
  • Start date Start date
  • Tags Tags
    Derivation
AI Thread Summary
The Sackur-Tetrode equation is derived as the classical limit of quantum statistics, specifically through Boltzmann statistics, which accounts for particle indistinguishability. Classical thermodynamics alone cannot derive this equation without encountering issues like the Gibbs paradox, leading to incorrect entropy expressions. The derivation involves applying Stirling's approximation to the multiplicity formula for an ideal gas. While it is possible to derive the equation without a macrocanonical ensemble, the assumption of indistinguishability is crucial, introducing a factor of 1/N! that is fundamentally quantum mechanical. Thus, the Sackur-Tetrode equation highlights the limitations of classical approaches in accurately describing entropy.
ralden
Messages
76
Reaction score
0
how sackur-tetrode equation derive?, can it derive without the use of macrocanonical ensemble? only by classical thermodynamics? thank you.
 
Physics news on Phys.org
The Sackur-Tetrode formula can only be derived properly as the classical limit of quantum statistics, which is Boltzmann statistics for both fermions and bosons, taking into account the indistinguishability of particles, which is a specific quantum-mechanical phenomenon. Classical statistics leads to the Gibbs paradoxon and a wrong (non-extensive) expression for the entropy which is solved by the Sackur-Tetrode formula.
 
You can derive the Sackur-Tetrode equation by solving for the entropy of an ideal gas using Stirling's approximation applied to the multiplicity formula. My thermodynamics text does not go through the whole derivation, but that is how it says to derive it.
 
Yes, that you can do, but you have to assume the indistinguishability of particles, which leads to an additional factor 1/N! compared to classical mechanics. This factor cannot justified without the indistinguishability argument that is generically quantum theoretical.
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »
Thread 'A scenario of non-uniform circular motion'

Thread 'A scenario of non-uniform circular motion'

(All the needed diagrams are posted below) My friend came up with the following scenario. Imagine a fixed point and a perfectly rigid rod of a certain length extending radially outwards from this fixed point(it is attached to the fixed point). To the free end of the fixed rod, an object is present and it is capable of changing it's speed(by thruster say or any convenient method. And ignore any resistance). It starts with a certain speed but say it's speed continuously increases as it goes...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »

Similar threads

I State functions in Grand Canonical Ensemble vs Canonical
Replies
3
Views
2K
Understanding the Differences Between Bose and Classical Gases
Replies
2
Views
1K
Thermodynamics of a Single-Component Ideal Gas
Replies
1
Views
1K
Thermal Physics: Thermodynamic Identity
Replies
10
Views
2K
I Question on derivation of a property of Poisson brackets
Replies
0
Views
1K
Ideal gas in the microcanonical ensemble - a subtle point?
Replies
14
Views
4K
Microcanonical ensemble generalized pressure
Replies
2
Views
984
How Does the Sackur-Tetrode Equation Resolve the Gibbs Paradox?
Replies
4
Views
5K
I Dispersion Relation in Different Media
Replies
3
Views
1K
I How Does Temperature Affect Wire Tension at Constant Length?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top