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

Relativistic mechanics and thermodynamics: part I. A linear-translation four-vector formalism

Einstein’s special theory of relativity is presented in a Minkowski four-vector formalism integrating mechanics and thermodynamics at a sophomore level, allowing the solution of undergraduate

Relativistic mechanics and thermodynamics: II. A linear translation Hamiltonian–Lagrangian formalism

A relativistic Hamiltonian–Lagrangian formalism for a composite system submitted to conservative and non-conservative forces is developed. A block descending an incline with a frictional force,

Relativistic solar sails

We apply the four-vector formalism of special relativity to describe various interaction processes of photons with a solar sail, in two cases: when the sail’s surface is a perfect mirror, and when it

Relativistic mechanics and thermodynamics. III. Rotation

A covariant four-tensor rotation equation—for bi-dimensional composite body—, by generalising cross product to four-vectors, is obtained. From it, a relativistic angular impulse-angular momentum

Four-vector description of the photon-in-a-box problem

The emission/absorption of a photon and the launch/capture of a massive particle in special relativity Einstein-like boxes are studied, using the four-vector formalism. The study demands the

Relativistic thermodynamics on conveyor belt

Two thermodynamic processes are analysed by using a relativistic four-vector fundamental equation formalism: the launching of a projectile by forces produced by chemical reactions inside a cannon

Dissipation effects in mechanics and thermodynamics

With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative

Relativistic description of the photoelectric effect

Einstein's famous explanation of the photoelectric effect is addressed using the Minkowski four-vector formalism. This formalism deals with energy and linear momentum simultaneously and it is Lorentz

On the relativistic lever paradox

As the ‘relativistic lever paradox’ is a characteristic topic in the theory of relativity application to rotation processes, a covariant four-tensor equation is developed to describe the relativistic

On the relativistic conveyor belt

A relativistic four-vector fundamental equation formalism is used to analyse processes that are carried out on a conveyor belt, in reference frames S (with the conveyor belt at rest, ground) and S¯

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

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

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

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

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

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

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

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

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

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

STOPPING OBJECTS WITH ZERO EXTERNAL WORK : MECHANICS MEETS THERMODYNAMICS

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,
...