Proving the Lorentz Invariance of the Entropy and the Covariance of Thermodynamics

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.

Gas and Dolomite Outbursts in Ore Mines—Analysis of the Phenomenon and the Energy Balance

In this paper, we present the problem of gas and dolomite outbursts in copper mines. The energy balance of the phenomenon is analyzed. An examination of the porosity of the dolomites is performed; in addition, the content and pressure of the gas accumulated in the pore structure of the rock are determined. The gas energy accumulated in the pore space of rocks is determined depending on the transformation occurring during gas decompression. The work needed to crush the rock for the grain distribution characteristic of post-outburst masses is examined. The gas energy needed to transport rocks is analyzed. The purpose of the research is to determine the limit values of parameters describing the gas and rock system for which there is a risk of dolomite and rock explosions. For the characteristic porosity of dolomites of −5%, gas and rock outbursts at 5 MPa pressure in isothermal transformation can be expected, and if the transformation is closer to adiabatic transformation, outbursts can be expected at 10 MPa pressure.

A model of gas flow with friction in a slotted seal

The paper discusses thermodynamic phenomena accompanying the flow of gas in a slotted seal. The analysis of the gas flow has been described based on an irreversible adiabatic transformation. A model based on the equation of total enthalpy balance has been proposed. The iterative process of the model aims at obtaining such a gas temperature distribution that will fulfill the continuity equation. The model allows for dissipation of the kinetic energy into friction heat by making use of the Blasius equation to determine the friction coefficient. Within the works, experimental research has been performed of the gas flow in a slotted seal of slot height 2 mm. Based on the experimental data, the equation of local friction coefficient was modified with a correction parameter. This parameter was described with the function of pressure ratio to obtain a mass flow of the value from the experiment. The reason for taking up of this problem is the absence of high accuracy models for calculating the gas flow in slotted seals. The proposed model allows an accurate determination of the mass flow in a slotted seal based on the geometry and gas initial and final parameters.