30
2 Macroscopic Thermodynamics
T 1 and T 2 . A slight variant of this argument is sometimes referred to as the Zeroth
Law of Thermodynamics, namely, if two systems are independently in thermal
equilibrium with a third system, then they are in thermal equilibrium with one
another. This result provides a means for the quantitative definition of temperature
through the third system serving as a thermometer.
As a thermodynamic (macroscopic) equilibrium system (similarly, its surroundings) will not tend to change state with time, it may be described in terms
of time-independent macroscopic, or thermodynamic, variables. Should any of
the conditions required for mechanical, chemical, or thermal equilibrium not
be satisfied, the system is said to be in a thermodynamic nonequilibrium state.
Nonequilibrium states are thus fundamentally different from equilibrium states in
that they cannot be described in terms of thermodynamic variables referring to the
system as a whole.
2.2 An Introduction to Thermodynamics
We shall focus our attention firstly upon the thermodynamics of pure substances. We
have seen in Sect. 1.2 3 that the equation of state for a macroscopic system consisting
of N classical ideal gas particles is
P V = Nk B T ,
(2.2.1)
relating the global thermodynamic properties P , V , and T . The ideal gas equation
of state thus constrains the allowed values of P , V , and T such that once any two
of them have been assigned (independent) values, the value of the third property is
fixed. An ideal gas consisting of N noninteracting particles can thus be described
thermodynamically via its equation of state.
We may rewrite Eq. (1.2.8) for the internal energy U(T ) of a classical ideal
monatomic gas as
U(T ) =
3
2 Nk B T ,
(2.2.2a)
from which it is clear that U is an extensive thermodynamic variable, as it is
proportional to the mass of the system via the number N of ideal gas particles. We
can also see from Eq. (2.2.2a) that the internal energy of such an ideal gas depends
only upon temperature and, in particular, does not depend upon volume. This means
that for an N -particle classical ideal gas, changes in the internal energy, dU , depend
only upon changes in temperature, dT , and hence
3 The first two values for a section or equation number identify chapter and section values
associated with that item.
2 Macroscopic Thermodynamics
T 1 and T 2 . A slight variant of this argument is sometimes referred to as the Zeroth
Law of Thermodynamics, namely, if two systems are independently in thermal
equilibrium with a third system, then they are in thermal equilibrium with one
another. This result provides a means for the quantitative definition of temperature
through the third system serving as a thermometer.
As a thermodynamic (macroscopic) equilibrium system (similarly, its surroundings) will not tend to change state with time, it may be described in terms
of time-independent macroscopic, or thermodynamic, variables. Should any of
the conditions required for mechanical, chemical, or thermal equilibrium not
be satisfied, the system is said to be in a thermodynamic nonequilibrium state.
Nonequilibrium states are thus fundamentally different from equilibrium states in
that they cannot be described in terms of thermodynamic variables referring to the
system as a whole.
2.2 An Introduction to Thermodynamics
We shall focus our attention firstly upon the thermodynamics of pure substances. We
have seen in Sect. 1.2 3 that the equation of state for a macroscopic system consisting
of N classical ideal gas particles is
P V = Nk B T ,
(2.2.1)
relating the global thermodynamic properties P , V , and T . The ideal gas equation
of state thus constrains the allowed values of P , V , and T such that once any two
of them have been assigned (independent) values, the value of the third property is
fixed. An ideal gas consisting of N noninteracting particles can thus be described
thermodynamically via its equation of state.
We may rewrite Eq. (1.2.8) for the internal energy U(T ) of a classical ideal
monatomic gas as
U(T ) =
3
2 Nk B T ,
(2.2.2a)
from which it is clear that U is an extensive thermodynamic variable, as it is
proportional to the mass of the system via the number N of ideal gas particles. We
can also see from Eq. (2.2.2a) that the internal energy of such an ideal gas depends
only upon temperature and, in particular, does not depend upon volume. This means
that for an N -particle classical ideal gas, changes in the internal energy, dU , depend
only upon changes in temperature, dT , and hence
3 The first two values for a section or equation number identify chapter and section values
associated with that item.