Nonequilibrium temperature measurement in a thermal conduction process

Puneet Kumar Patra and Romesh C. Batra
Phys. Rev. E 95, 013302 – Published 10 January 2017

Abstract

We identify the temperature being measured by a thermometer in a nonequilibrium scenario by studying heat conduction in a three-dimensional Lennard-Jones (LJ) system whose two ends are kept at different temperatures. It is accomplished by modeling the thermometer particles also with the LJ potential but with added tethers to prevent their rigid body motion. These models of the system and the thermometer mimic a real scenario in which a mechanical thermometer is “inserted” into a system and kept there long enough for the temperature to reach a steady value. The system is divided into five strips, and for each strip the temperature is measured using an embedded thermometer. Unlike previous works, these thermometers are small enough not to alter the steady state of the nonequilibrium system. After showing initial transients, the thermometers eventually show steady-state conditions with the subregions of the system and provide values of the different temperature definitions—kinetic, configurational, dynamical, and higher-order configurational. It is found that their kinetic and the configurational temperatures are close to the system's kinetic temperature except in the two thermostatted regions. In the thermostatted regions, where the system's kinetic and the configurational temperatures are significantly different, the thermometers register a temperature substantially different from either of these two values. With a decrease in the system density and size, these differences between the kinetic and the configurational temperatures of the thermometer become more pronounced.

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  • Received 16 July 2016

DOI:https://doi.org/10.1103/PhysRevE.95.013302

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Puneet Kumar Patra* and Romesh C. Batra

  • Department of Biomedical Engineering and Mechanics, M/C 0219, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

  • *pkpatra@vt.edu
  • rbatra@vt.edu

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Issue

Vol. 95, Iss. 1 — January 2017

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