Entropy and the Experience of Heat

Abstract

We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of an experientially natural approach might be-to this end we investigate and describe in some detail (a) how humans experience and conceptualize an extensive thermal quantity (i.e., an amount of heat), and (b) how this concept evolved during the early development of the science of thermal phenomena (beginning with the Experimenters of the Accademia del Cimento and ending with Sadi Carnot). We show that a direct approach to entropy, as the extensive quantity of models of thermal systems and processes, is possible and how it can be applied to the teaching of thermodynamics for various audiences.

Keywords: conceptualization; early history of thermal physics; entropy; extensive quantity of heat; phenomenology; teaching and learning of thermodynamics.

Figure 1

Left: experimental setup for measuring the artificial freezing of different liquids (the bulb on the left contains the liquid to be frozen; the bulb on the right containing alcohol is the Experimenters’ thermometer). Right top: an example of the data concerning the level of water in one of the bulbs and alcohol in the second (serving as the thermometer). Right bottom: diagram of the complete list of results reported for the level of alcohol in the neck of the second bulb, as a function of time (Vibrations), plus an exponentially decaying fitting curve (Source: [24], original page numbers included in the images).

Figure 2

Process diagram for a real pump operating in steady-state, showing the action and interaction of forces of nature using visual metaphors for intensities (potentials, vertical levels), flows of extensive quantities (lines with arrows), production rate of entropy (circle with dot), power (vertical fat arrows inside rectangle; downward arrow symbolizes rate of energy made available, upward arrows denote energy used), and energy transfers (fat horizontal arrows). The gray rectangle denotes the pump as a background upon which the forces are active. (Source: Adapted from [2], Figure 2.7, p. 54).

Figure 3

Process diagrams representing different (steady-state) processes caused by a fall of entropy through a temperature difference. 1: “Generic waterfall image” of a causing thermal process where we leave open what might follow. 2: Process diagram of an idea (Carnot) of a heat engine (an angular momentum current $I_L$ is “pumped” through its associated potential difference). 3: Total dissipation in heat transfer through a thermal resistor. 4: Real heat engine where energy made available is used for pumping angular momentum and producing entropy.

Figure 4

Simplest possible lumped parameter (uniform) dynamical model of a Peltier device. Thermally and electrically high and low faces are represented by capacitive elements. Transports of entropy ($I_S$, $I_{S,TE}$) and of charge ($I_Q$) take place between these capacitors. Entropy flows conductively, is carried by charge, and is produced (${\Pi }_S$; source symbol at top center). A temperature difference sets up a thermoelectric voltage $U_{TE}$ (“electromotoric force”). Adapted from [52], Figure 5.

Figure 5

Measuring entropy quantities. Left: the experimental set-up. Right: A typical result.