Efusividad Termica

Thermal Physics Concepts:
The Role of the Thermal
Effusivity
E. Marín, Universidad de La Habana, La Habana, Cuba

I

nspired by a previously published TPT article,1
this paper describes the concept of thermal effusivity and the role of this parameter in understanding thermal physics concepts, in particular the
fact that when we touch objects of equal temperature
but of differentmaterials we often feel that one body
is “hotter” or “colder.”
In the above mentioned article, Yeo and Zadnik
present an instrument to assess in students a wide
range of beliefs or understandings about thermodynamic concepts. Their “Thermal Concept Evaluation”
consists basically of a questionnaire with 26 multiplechoice items about heat energy and temperature, allowing students to apply eithereveryday physics or
classroom physics in their responses. In question 16
(see Fig. 2 in Ref. 1) students are asked about the preferred explanation of the following situation:
Kim takes a metal ruler and a wooden ruler
from a pencil case. He announces that the metal
one feels colder than the wooden one.
The authors of the paper suggest that of the five possible responses, the best explanation ofthe described
effect is that metal conducts energy away from his hand
more rapidly than wood. This assertion, in our opinion, can lead to the mistaken notion that the relevant
thermophysical parameter for the described phenomenon is the very well-known thermal conductivity k
instead of the thermal effusivity , whose role is usually undervalued and/or misunderstood, but which
can be exploitedin advanced introductory physics
432

courses, especially at the high school level, where the
analysis of energy transport problems presented in
standard textbooks does not make any use of its concept. Therefore, it is the objective of this paper to discuss briefly the meaning of this parameter and its role
in transient heating phenomena. For this purpose we
will make use of the exampledescribed above.
Thermal effusivity, also called “contact coefficient”
by some authors,2 is defined as

ε = kρc = k

α

= ρc α ,

(1)

where α is the thermal diffusivity, ρ the mass density,
and c the specific heat.3 An extended explanation of
the physical relevance of the parameters governing
the generation and propagation of heat energy in
solids can be found in many books,monographs, and
articles.4-7
Thermal conductivity is defined by Fourier’s law of
heat energy conduction8 and measures the energy flow
per unit time through a unit area of a unit thickness
of a material that has a unit temperature difference
between its opposite faces. On the other hand, a timevarying phenomenon is described by the differential
equation of thermal diffusion9 (energy conservationlaw), also requiring knowledge of the thermal diffusivity and effusivity. The former is the quantity associated
with the speed of propagation of energy in a material
as its temperature changes. If the changes are periodic,
the thermal effusivity comes into play, determining
the magnitude of the temperature at the solid surface.
In this case, the temperature field behaves as an at-

DOI:10.1119/1.2353583

THE PHYSICS TEACHER ◆ Vol. 44, October 2 006

Table I. Thermal properties of different homogeneous solids at room temperature.

34

hard wood

32

PVC

Tc (oC)

ε(J.m-2.
K-1.s-1/2)

Material

24

Pb

Co

22

K

20
0

1

Cu

64,040

1.78

116

37,140

3.45

102

158

8150

0.65

100

24.6

20,150

4.05

ρc (x 10-6J/m3.K)

Ni

3

4

5

6

7

ε(x 104J . m-2 . K-1 . s-1/2)
Fig. 1. Contact or feeling temperature between human
skin at 37oC and different bodies at 20oC as a function
of their thermal effusivities [from Eq. (2)].

tenuated plane wave well known as a thermal wave.6,7
The concept of thermal wave first appeared about a
hundred years ago when Fourier10 showed that heat
conduction...