# Relativistic mechanical–thermodynamical formalism—description of inelastic collisions

@article{Gmez2016RelativisticMF, title={Relativistic mechanical–thermodynamical formalism—description of inelastic collisions}, author={J G{\"u}{\'e}mez and M Fiolhais and L. A. Fern{\'a}ndez}, journal={European Journal of Physics}, year={2016}, volume={37} }

We present a relativistic formalism inspired by the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single particle, but is also related to the classical treatment of problems that require both Newton's second law and the energy conservation law. We apply the developed formalism to inelastic collisions to better show how it works.

## 10 Citations

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## References

SHOWING 1-10 OF 55 REFERENCES

### Explicit derivation of the relativistic mass–energy relation for internal kinetic and potential energies of a composite system

- Physics
- 2005

A straightforward derivation of relativistic expressions for the mechanical momentum, kinetic and total energies, and mass–energy equivalence (including potential energy) which does not require any…

### Lorentz transformation of thermodynamic quantities: II

- Physics
- 1967

Relativistic transformation formulae for thermodynamic quantities are obtained here without having recourse to integrations in the phase space. The controversial role of the Jacobians of…

### From mechanics to thermodynamics—analysis of selected examples

- Physics
- 2013

We present and discuss a selection of classical mechanics and thermodynamics problems. The discussion is based on the use of the impulse–momentum equation simultaneously with the centre-of-mass…

### Manifestly covariant formulation of Bohr's theory for photon emission from an atom

- Physics
- 1980

The equation for the frequencies of light emitted by a hydrogen atom is written in a manifestly covariant way. It is shown that the covariant equation resolves a 'relativistic paradox' formulated by…

### Note on the relativistic elastic head-on collision

- Physics
- 2002

A short, elegant, instructive, and explicit solution for the relativistic elastic head-on collision is presented. It uses the invariance of the relative speed and a suitable Lorentz transformation of…

### How to explain the non-zero mass of electromagnetic radiation consisting of zero-mass photons

- Physics
- 2007

The mass of electromagnetic radiation in a cavity is considered using the correct relativistic approach based on the concept of a scalar mass not dependent on the particle (system) velocity. It is…

### The mass of a gas of massless photons

- Physics
- 1995

Using minimal formalism, we demonstrate that the massless photons, constituting the radiation in a cavity, contribute to the mass of the cavity in agreement with Einstein’s mass–energy formula. We…

### Einstein and statistical thermodynamics. I. Relativistic thermodynamics

- Physics, Chemistry
- 1981

The influence of Einstein on statistical thermodynamics is illustrated by considering, from both the historical and a modern point of view, the relativistic transformation of thermodynamic quantities.

### The Special Theory of Relativity: A Mathematical Approach

- Biology, Physics
- 2014

Pre-Relativity and Galilean Transformation, Lorentz Transformations, Relativistic Mechanics of continua, and Four Dimensional World.

### STOPPING OBJECTS WITH ZERO EXTERNAL WORK : MECHANICS MEETS THERMODYNAMICS

- Physics
- 1993

Although the work‐energy theorem of pure, nondissipative mechanics states that the work done stopping a body equals its kinetic energy change, the work done stopping a body via an inelastic,…