“加热冷却”--展示纵向specific heat的重要性
"Cooling by heating" - demonstrating the significance of the longitudinal specific heat
摘要：
在表面加热固体球体会在球体内部产生机械应力。如果提供有限的热量，随着温度在整个球体上变得均匀，应力逐渐消失。我们表明，在此之前发生，有一个暂时的压力和密度在球体内部的降低，诱导一个短暂的温度降低。对于普通固体，这种影响很小，因为c_p几乎等于c_V。对于流动液体，这种影响可以忽略，因为它们的动态剪切模量为零。然而，对于处于玻璃化转变的液体，这种影响通常比固体大得多。本文给出了相应的耦合热粘弹性方程的解析解。通常，在恒压下测得的等压比热c_p和纵向比热c_l之间存在差异，这与限制相关膨胀为纵向的机械边界条件有关。在热传播的精确处理的热扩散常数包含C_L，而不是C_P。我们表明，控制的“冷却加热”效应的大小的关键参数是这两个比热之间的相对差异。对于典型的玻璃形成液体，当表面温度增加1 K时，如果在玻璃化转变下进行实验，则预期球心温度降低5 mK级。通过在玻璃化转变时对直径为19 mm的葡萄糖球进行测量，证实了加热冷却效应。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
