Christian Gruber

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Lagrange Equations Coupled to a Thermal Equation: Mechanics as Consequence of Thermodynamics

Sylvain Bréchet, Christian Gruber

Following the analytic approach to thermodynamics developed by Stuckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential.

MDPI AG2011

Friction force: from mechanics to thermodynamics

Christian Ferrari, Christian Gruber

We study some mechanical problems in which a friction force is acting on a system. Using the fundamental concepts of state, time evolution and energy conservation, we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of thermodynamics and then apply them to investigate the time evolution and heat transfer of some significant examples.

2010

In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365–6) ('length contraction paradox'), a rigid rod moves at high speed over a table towards a hole of the same size. A bystander expects the rod to fall into the hole, but a co-moving observer expects it to pass unhindered over the hole. According to the accepted solution as first described in that paper, the entire rod must fall somewhat into the hole and therefore cannot remain rigid when the hole moves underneath it. We present an improved approach that is based on retardation due to speed of stress propagation, and in which proper stiffness is not affected. After showing how to solve the similar but simpler car and hole paradox, we find with the same approach that the rod as depicted in Rindler's paper will not fall into the hole as was claimed and that it may pass practically unhindered over it.

2005