• DOI:10.1103/PhysRevX.2.041015
• Corpus ID: 53414775

"Cooling by heating" - demonstrating the significance of the longitudinal specific heat

@article{Papini2012CoolingBH,
  title={"Cooling by heating" - demonstrating the significance of the longitudinal specific heat},
  author={Jon J. Papini and Jeppe C. Dyre and Tage Emil Christensen},
  journal={arXiv: Soft Condensed Matter},
  year={2012}
}

• J. Papini, J. Dyre, T. Christensen
• Published 26 June 2012
• Physics
• arXiv: Soft Condensed Matter

Heating a solid sphere at the surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because c_p is almost equal to c_V. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat, c_p, measured at constant isotropic pressure and the longitudinal specific heat, c_l, pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation the heat diffusion constant contains c_l rather than c_p. We show that the key parameter controlling the magnitude of the "cooling-by-heating" effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when temperature at the surface is increased by 1 K, a lowering of the temperature in the sphere center of order 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a 19 mm diameter glucose sphere at the glass transition.