Thermodynamics and Chemistry

CHAPTER 2 SYSTEMS AND THEIR PROPERTIES

2.5 PROCESSES ANDPATHS 50

TD 400 K TD 300 K

TD 350 K

Figure 2.8 Steady state in a metal rod (shaded) with heat conduction. The boxes at

the ends represent heat reservoirs of constant temperature.

3.The concept of an equilibrium state assumes that when the system is in this state and

isolated, no observable change occurs during the period of experimental observation.

If the state does, in fact, undergo a slow change that is too small to be detected during

the experimental observation periodÅtexp, the state ismetastable—the relaxation

time of the slow change is much greater thanÅtexp. There is actually no such thing

as a true equilibrium state, because very slow changes inevitably take place that we

have no way of controlling. One example was mentioned above: the slow formation

of water from its elements in the absence of a catalyst. Atoms of radioactive elements

with long half-lives slowly change to other elements. More generally, all elements are

presumably subject to eventual transmutation to iron-58 or nickel-62, the nuclei with

the greatest binding energy per nucleon. When we use the concept of an equilibrium

state, we are in effect assuming that rapid changes that have come to equilibrium

have relaxation times much shorter thanÅtexpand that the relaxation times of all

other changes are infinite.

2.4.5 Steady states

It is important not to confuse an equilibrium state with asteady state, a state that is con-
stant during a time period during which the system exchanges matter or energy with the
surroundings.
The heat-conducting metal rod shown in Fig.2.8is a system in such a steady state.
Each end of the rod is in thermal contact with aheat reservoir(orthermal reservoir),
which is a body or external system whose temperature remains constant and uniform when
there is heat transfer to or from it.^12 The two heat reservoirs in the figure have different
temperatures, causing a temperature gradient to form along the length of the rod and energy
to be transferred by heat from the warmer reservoir to the rod and from the rod to the cooler
reservoir. Although the properties of the steady state of the rod remain constant, the rod is
clearly not in an equilibrium state because the temperature gradient will quickly disappear
when we isolate the rod by removing it from contact with the heat reservoirs.

2.5 Processes and Paths

Aprocessis a change in the state of the system over time, starting with a definite initial
state and ending with a definite final state. The process is defined by apath, which is the

(^12) A heat reservoir can be a body that is so large that its temperature changes only imperceptibly during heat
transfer; a thermostat bath whose temperature can be controlled; or an external system of coexisting phases of
a pure substance (e.g., ice and water) at constant pressure.