evolved, with further clarification of the second law of “thermodynamics,” into
modern thermodynamics and statistical mechanics.
At this early point of discourse, we need not to be concerned with the precise
nature of heat, only with what we can do with heat. Planck described the goal of his
treatise [3] being to offer a uniform viewpoint for the entire field and, for that
purpose, his method was “distinct from the other two, in that it does not advance the
mechanical theory of heat, but, keeping aloof from definite assumptions as to its
nature, starts direct[ly] from a few very general empirical facts, mainly the two
fundamental principles of Thermodynamics.” I share with Planck the goal in seeking
a uniform point of view for the entire field: rather than aiming for a unity of science
(i.e., reductionism), the goal is for a unity of knowledge (consilience as originally
defined by Whewell), which is a less lofty goal but one reachable and still deeply
satisfactory. By having a good idea of what we can do with heat, we shall have a
good understanding of heat, even in absence of a precisely worded definition.
The conception of heat arises from the sensation of warmth or coldness, which is
immediately experienced upon touching the surface of a body. This direct sensation, however, furnishes no quantitative scientific measure of a body’s state with
regard to heat; it yields only qualitative impressions of warmth or coldness, which
vary according to external circumstances and subjective perceptions. For quantitative purposes, we utilize the change of volume which takes place in all bodies
when heated under constant pressure, for this admits of exact measurement. Heating
produces in most substances and under most conditions an increase of volume, and
thus we can tell whether a body gets hotter or colder with a quantitative yardstick, a
purely mechanical observation affording a much higher degree of precision.
If two bodies, one of which feels colder than the other, are brought together (for
example, a good size ice cube and warm water), it is invariably found that the
warmer (or hotter) body is cooled to, and the colder one heated up to a certain point,
and then change ceases. The two bodies are then said to be in thermal equilibrium.
Experience shows that such a state of general equilibrium sets in, not only when
two, but also when any number of bodies initially at different degrees of warmth (or
coldness) are brought into mutual contact. From this follows the proposition,
known as the zeroth law of thermodynamics (see Fig. 1.1):
If a body, A, be in thermal equilibrium with another body, B, and with a second different
body C, then B and C are in thermal equilibrium with one another.
For, if we bring A, B, and C together so that each touches the other two, then,
according to our supposition of thermal equilibrium, there will be equilibrium at the
points of contact AB and AC, and, therefore, also at the contact BC. If it were not so,
no general thermal equilibrium would be possible, which is contrary to experience.
These facts enable us to compare the degree of heat of two bodies, B and C,
without having to bring them into direct contact but by bringing each body into
contact of an arbitrarily selected third body, A. This third standard body, for
example, can be a column of mercury enclosed in a vessel of capillary tube and
bulb. By observing the volume of A (height of mercury in the case of capillary tube
mercury thermometer) in each case, it is possible to tell whether B and C are in
1.2 Thermal Equilibrium and Temperature
5
modern thermodynamics and statistical mechanics.
At this early point of discourse, we need not to be concerned with the precise
nature of heat, only with what we can do with heat. Planck described the goal of his
treatise [3] being to offer a uniform viewpoint for the entire field and, for that
purpose, his method was “distinct from the other two, in that it does not advance the
mechanical theory of heat, but, keeping aloof from definite assumptions as to its
nature, starts direct[ly] from a few very general empirical facts, mainly the two
fundamental principles of Thermodynamics.” I share with Planck the goal in seeking
a uniform point of view for the entire field: rather than aiming for a unity of science
(i.e., reductionism), the goal is for a unity of knowledge (consilience as originally
defined by Whewell), which is a less lofty goal but one reachable and still deeply
satisfactory. By having a good idea of what we can do with heat, we shall have a
good understanding of heat, even in absence of a precisely worded definition.
The conception of heat arises from the sensation of warmth or coldness, which is
immediately experienced upon touching the surface of a body. This direct sensation, however, furnishes no quantitative scientific measure of a body’s state with
regard to heat; it yields only qualitative impressions of warmth or coldness, which
vary according to external circumstances and subjective perceptions. For quantitative purposes, we utilize the change of volume which takes place in all bodies
when heated under constant pressure, for this admits of exact measurement. Heating
produces in most substances and under most conditions an increase of volume, and
thus we can tell whether a body gets hotter or colder with a quantitative yardstick, a
purely mechanical observation affording a much higher degree of precision.
If two bodies, one of which feels colder than the other, are brought together (for
example, a good size ice cube and warm water), it is invariably found that the
warmer (or hotter) body is cooled to, and the colder one heated up to a certain point,
and then change ceases. The two bodies are then said to be in thermal equilibrium.
Experience shows that such a state of general equilibrium sets in, not only when
two, but also when any number of bodies initially at different degrees of warmth (or
coldness) are brought into mutual contact. From this follows the proposition,
known as the zeroth law of thermodynamics (see Fig. 1.1):
If a body, A, be in thermal equilibrium with another body, B, and with a second different
body C, then B and C are in thermal equilibrium with one another.
For, if we bring A, B, and C together so that each touches the other two, then,
according to our supposition of thermal equilibrium, there will be equilibrium at the
points of contact AB and AC, and, therefore, also at the contact BC. If it were not so,
no general thermal equilibrium would be possible, which is contrary to experience.
These facts enable us to compare the degree of heat of two bodies, B and C,
without having to bring them into direct contact but by bringing each body into
contact of an arbitrarily selected third body, A. This third standard body, for
example, can be a column of mercury enclosed in a vessel of capillary tube and
bulb. By observing the volume of A (height of mercury in the case of capillary tube
mercury thermometer) in each case, it is possible to tell whether B and C are in
1.2 Thermal Equilibrium and Temperature
5