# Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only

@article{RomeroRochn2020DerivationOT, title={Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only}, author={V{\'i}ctor Romero-Roch{\'i}n}, journal={Entropy}, year={2020}, volume={22} }

Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and therefore all free energies, do obey scaling. Although we limit ourselves to such a system, we elaborate about the possibilities of finding universality…

## One Citation

### Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

- PhysicsEntropy
- 2021

This work shows that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom, and predicts that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve.

## References

SHOWING 1-10 OF 27 REFERENCES

### The theory of equilibrium critical phenomena

- Physics
- 1967

The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their…

### Inequality for the specific heat: I. Derivation

- Mathematics
- 1967

A rigorous inequality is derived relating the specific heat of a system, the temperature derivative of the expectation value of an arbitrary operator and the mean-square fluctuation of the operator…

### Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

- Physics, Mathematics
- 1952

The problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent. From this equivalence an example of a two-dimensional lattice gas is given for which the…

### Equation of State in the Neighborhood of the Critical Point

- Mathematics
- 1965

A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an…

### Entropy geometric construction of a pure substance with normal, superfluid and supersolid phases

- Physics
- 2016

Using the laws of thermodynamics together with empirical data, we present a qualitative geometric construction of the fundamental relation of a pure substance $S = S(E,N,V)$, with $S$ entropy, $E$…

### Field Theory, the Renormalization Group, and Critical Phenomena: Graphs to Computers

- Physics
- 1978

Pertinent Concepts and Ideas in the Theory of Critical Phenomena Formulation of the Problem of Phase Transitions in Terms of Functional Integrals Functional Integrals in Quantum Field Theory…

### Specific heat of liquid helium in zero gravity very near the lambda point

- Physics
- 2003

We report the details and revised analysis of an experiment to measure the specific heat of helium with subnanokelvin temperature resolution near the lambda point. The measurements were made at the…

### Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation

- Physics
- 1952

A theory of equations of state and phase transitions is developed that describes the condensed as well as the gas phases and the transition regions. The thermodynamic properties of an infinite sample…