An undergraduate exercise in the first law of relativistic thermodynamics

Abstract

The isothermal compression of an ideal gas is analysed using a relativistic thermodynamics formalism based on the principle of inertia of energy (Einstein's equation) and the asynchronous formulation (Cavalleri and Salgarelli 1969 Nuovo Cimento 42 722–54), which is similar to the formalism developed by van Kampen (1968 Phys. Rev. 173 295–301) and Hamity (1969 Phys. Rev. 187 1745–52). In this 4-vector Minkowski formalism mechanical and thermodynamical processes are described by the first law of thermodynamics expressed as ΔUμ = Wμ + Qμ, in a Lorentz covariant way. This exercise is considered useful for undergraduate physics students interested in foundations of physics, with the only prerequisites in first courses in thermodynamics and special relativity.