CHAPTER 4 THE SECOND LAW
4.2 STATEMENTS OF THESECONDLAW 102
It is true that reversible processes and purely mechanical processes are idealized pro-
cesses that cannot occur in practice, but a spontaneous process can bepracticallyreversible
if carried out sufficiently slowly, orpracticallypurely mechanical if friction and temperature
gradients are negligible. In that sense, they are not impossible processes. This book will
reserve the term “impossible” for a process that cannot be approached by any spontaneous
process, no matter how slowly or how carefully it is carried out.
4.2 Statements of the Second Law
A description of themathematical statement of the second lawis given in the box below.
dSD∂q=Tbfor a reversible change of a closed system;
dS > ∂q=Tbfor an irreversible change of a closed system;
whereSis an extensive state function, the entropy, and
∂qis an infinitesimal quantity of energy transferred
by heat at a portion of the boundary where the
thermodynamic temperature isTb.The box includes three distinct parts. First, there is the assertion that a property called
entropy,S, is an extensive state function. Second, there is an equation for calculating
the entropy change of a closed system during a reversible change of state: dSis equal to
∂q=Tb.^1 Third, there is a criterion for spontaneity: dSis greater than∂q=Tbduring an
irreversible change of state. The temperatureTbis a thermodynamic temperature, which
will be defined in Sec.4.3.4.
Each of the three parts is an essential component of the second law, but is somewhat
abstract. What fundamental principle, based on experimental observation, may we take
as the starting point to obtain them? Two principles are available, one associated with
Clausius and the other with Kelvin and Planck. Both principles are equivalent statements of
the second law. Each asserts that a certain kind of process is impossible, in agreement with
common experience.
Consider the process depicted in Fig.4.1(a) on the next page. The system is isolated,
and consists of a cool body in thermal contact with a warm body. During the process, energy
is transferred by means of heat from the cool to the warm body, causing the temperature of
the cool body to decrease and that of the warm body to increase. Of course, this process
is impossible; we never observe heat flow from a cooler to a warmer body. (In contrast,
the reverse process, heat transfer from the warmer to the cooler body, is spontaneous and
irreversible.) Note that this impossible process does not violate the first law, because energy
is conserved.
Suppose we attempt to bring about the same changes in the two bodies by interposing a
device of some sort between them, as depicted in Fig.4.1(b). Here is how we would like the
device to operate in the isolated system: Heat should flow from the cool body to the device,
(^1) During a reversible process, the temperature usually has the same valueTthroughout the system, in which case
we can simply write dSD∂q=T. The equation dSD∂q=Tballows for the possibility that in an equilibrium
state the system has phases of different temperatures separated by internal adiabatic partitions.