discussed in Chap. 4 (see Footnote 1) and afterward, there is no irreversibility if the
world is at equilibrium. It is also impossible to be away from equilibrium without
any manifestation of irreversibility. We study thermodynamics and NET because of
the irreversibility and interconnectedness of nature, and the driving forces resulting
from irreversibility manifested in the tendency toward equilibrium.
1.4 Dimension and Unit of Temperature
A macroscopic description of a system may be expressed in terms of its extensive
state variables—mass and volume—and its intensive state variables—pressure and
temperature. An intensive state variable is the macroscopic manifestation of
microscopic processes of individual atoms and molecules. Pressure is the macroscopic manifestation of particle momentum transfer; its dimension is force per unit
area (FL
−2 , or ML
−1 T
−2 , with unit N/m
2 or kN/m
2 ). Temperature is the macroscopic manifestation of particle kinetic energy (the average particle kinetic energy).
This might suggest that temperature could also be defined in terms of energy.
However, temperature is not only the “quantitative” sum of single particles’ energy
but also the “qualitative” characterization of the collective distribution of particle
energies. Therefore, such a suggestion would have been mistaken.
2
The general concept of temperature logically follows from the postulate of
thermal equilibrium, and following R. H. Fowler, the postulate is known as the
zeroth law of thermodynamics (Sect. 1.2). Temperature, therefore, is strictly a
macroscopic concept. The thermodynamic concept of temperature, in fact, was
rigorously developed from the concept of Carnot’s temperature function by Carnot
and Kelvin. Unlike pressure, which is a derived dimension in terms of the three
fundamental dimensions of mechanics, the dimension of temperature is a new
fundamental dimension, which together with the three fundamental dimensions of
mechanics defines the four fundamental dimensions of thermodynamics. Consequently, as we shall see in the following chapters, heat and thermal energy (which is
a function of temperature)—though quantitatively equivalent to––are qualitatively
different from work and mechanical energy (both of which are independent of
temperature), respectively.
2
This discussion of temperature follows the conventional approach, which preceded the
introduction of entropy. That is, once the dimension of temperature was determined, the
dimension of entropy was linked via its definition to the dimension of temperature. Reassessment
of the meaning of temperature and entropy in recent years has led to the suggestion that entropy
should be dimensionless, and temperature, correspondingly, is then redefined as tempergy—which
has the dimension of energy. [H. S. Leff (1999) Am. J. Phys. 67(12):1114–1122].
This is an interesting reinterpretation. A dimensionless reduced entropy and an energy-dimension
tempergy, however, do not infer that there is no need for a new dimension for the conjugate pair of
tempergy-reduced entropy or temperature-entropy. What is significant is the existence of a new
FUNDAMENTAL DIMENSION with the introduction of the conjugate pair.
1.3 Thermodynamic Systems and the General Concept of Equilibrium
9
world is at equilibrium. It is also impossible to be away from equilibrium without
any manifestation of irreversibility. We study thermodynamics and NET because of
the irreversibility and interconnectedness of nature, and the driving forces resulting
from irreversibility manifested in the tendency toward equilibrium.
1.4 Dimension and Unit of Temperature
A macroscopic description of a system may be expressed in terms of its extensive
state variables—mass and volume—and its intensive state variables—pressure and
temperature. An intensive state variable is the macroscopic manifestation of
microscopic processes of individual atoms and molecules. Pressure is the macroscopic manifestation of particle momentum transfer; its dimension is force per unit
area (FL
−2 , or ML
−1 T
−2 , with unit N/m
2 or kN/m
2 ). Temperature is the macroscopic manifestation of particle kinetic energy (the average particle kinetic energy).
This might suggest that temperature could also be defined in terms of energy.
However, temperature is not only the “quantitative” sum of single particles’ energy
but also the “qualitative” characterization of the collective distribution of particle
energies. Therefore, such a suggestion would have been mistaken.
2
The general concept of temperature logically follows from the postulate of
thermal equilibrium, and following R. H. Fowler, the postulate is known as the
zeroth law of thermodynamics (Sect. 1.2). Temperature, therefore, is strictly a
macroscopic concept. The thermodynamic concept of temperature, in fact, was
rigorously developed from the concept of Carnot’s temperature function by Carnot
and Kelvin. Unlike pressure, which is a derived dimension in terms of the three
fundamental dimensions of mechanics, the dimension of temperature is a new
fundamental dimension, which together with the three fundamental dimensions of
mechanics defines the four fundamental dimensions of thermodynamics. Consequently, as we shall see in the following chapters, heat and thermal energy (which is
a function of temperature)—though quantitatively equivalent to––are qualitatively
different from work and mechanical energy (both of which are independent of
temperature), respectively.
2
This discussion of temperature follows the conventional approach, which preceded the
introduction of entropy. That is, once the dimension of temperature was determined, the
dimension of entropy was linked via its definition to the dimension of temperature. Reassessment
of the meaning of temperature and entropy in recent years has led to the suggestion that entropy
should be dimensionless, and temperature, correspondingly, is then redefined as tempergy—which
has the dimension of energy. [H. S. Leff (1999) Am. J. Phys. 67(12):1114–1122].
This is an interesting reinterpretation. A dimensionless reduced entropy and an energy-dimension
tempergy, however, do not infer that there is no need for a new dimension for the conjugate pair of
tempergy-reduced entropy or temperature-entropy. What is significant is the existence of a new
FUNDAMENTAL DIMENSION with the introduction of the conjugate pair.
1.3 Thermodynamic Systems and the General Concept of Equilibrium
9