Page 53 - Physical chemistry eng

30 CHAPTER 2 Heat, Work, Internal Energy, Enthalpy, and the First Law of Thermodynamics

1000
800
T/K 400
600
200 2.7 Equilibrium, Change, and Reversibility
3
Thermodynamics can only be applied to systems in internal equilibrium, and a require-
P/(10 6 Pa) or chemical reaction be zero. How do we reconcile these statements with our calcula-
2 ment for equilibrium is that the overall rate of change of all processes such as diffusion
i
f 1 tions of q, w, and ¢U associated with processes in which there is a macroscopic change
in the system? To answer this question, it is important to distinguish between the sys-
0 tem and surroundings each being in internal equilibrium, and the system and surround-
12.5 10 7.5 5.0 2.5 ings being in equilibrium with one another.
V/L We first discuss the issue of internal equilibrium. Consider a system made up of an
ideal gas, which satisfies the equation of state, P = nRT>V . All combinations of P, V,
FIGURE 2.12
and T consistent with this equation of state form a surface in P–V–T space as shown in
All combinations of pressure, volume,
and temperature consistent with 1 mol of Figure 2.12. All points on the surface correspond to states of internal equilibrium, mean-
an ideal gas lie on the colored surface. All ing that the system is uniform on all length scales and is characterized by single values of
combinations of pressure and volume T, P, and concentration. Points that are not on the surface do not correspond to any equi-
consistent with T = 800 K and all combi- librium state of the system because the equation of state is not satisfied. Nonequilibrium
nations of pressure and temperature con- situations cannot be represented on such a plot, because T, P, and concentration do not
sistent with a volume of 4.0 L are shown have unique values for a system that is not in equilibrium. An example of a system that is
as black curves that lie in the P–V–T sur-
not in internal equilibrium is a gas that is expanding so rapidly that different regions of
face. The third curve corresponds to a
the gas have different values for the density, pressure, and temperature.
path between an initial state i and a final
Next, consider a process in which the system changes from an initial state charac-
state f that is neither a constant tempera-
terized by P , V , and T to a final state characterized by P , V , and T as shown in
ture nor a constant volume path. i i i f f f
Figure 2.12. If the rate of change of the macroscopic variables is negligibly small, the
system passes through a succession of states of internal equilibrium as it goes from the
initial to the final state. Such a process is called a quasi-static process, in which inter-
nal equilibrium is maintained in the system. If the rate of change is large, the rates of
diffusion and intermolecular collisions may not be high enough to maintain the system
in a state of internal equilibrium. Thermodynamic calculations for such a process are
valid only if it is meaningful to assign a single value of the macroscopic variables P, V, T,
and concentration to the system undergoing change. The same considerations hold for
the surroundings. We only consider quasi-static processes in this text.
We now visualize a process in which the system undergoes a major change in
terms of a directed path consisting of a sequence of quasi-static processes, and distin-
guish between two very important classes of quasi-static processes, namely reversible
Pulley
and irreversible processes. It is useful to consider the mechanical system shown in
Figure 2.13 when discussing reversible and irreversible processes. Because the two
masses have the same value, the net force acting on each end of the wire is zero, and
the masses will not move. If an additional mass is placed on either of the two masses,
the system is no longer in mechanical equilibrium, and the masses will move. In the
limit in which the incremental mass approaches zero, the velocity at which the initial
masses move approaches zero. In this case, one refers to the process as being
reversible, meaning that the direction of the process can be reversed by placing the
infinitesimal mass on the other side of the pulley.
Reversibility in a chemical system can be illustrated by a system consisting of liq-
uid water in equilibrium with gaseous water that is surrounded by a thermal reservoir.
1 kg
The system and surroundings are both at temperature T. An infinitesimally small
increase in T results in a small increase of the amount of water in the gaseous phase,
and a small decrease in the liquid phase. An equally small decrease in the temperature
has the opposite effect. Therefore, fluctuations in T give rise to corresponding fluctua-
1 kg tions in the composition of the system. If an infinitesimal opposing change in the vari-
able that drives the process (temperature in this case) causes a reversal in the direction
FIGURE 2.13
Two masses of exactly 1 kg each are con- of the process, the process is reversible.
nected by a wire of zero mass running If an infinitesimal change in the driving variable does not change the direction of
over a frictionless pulley. The system is in the process, one says that the process is irreversible. For example, if a large stepwise
mechanical equilibrium and the masses temperature increase is induced in the system using a heat pulse, the amount of water in
are stationary. the gas phase increases abruptly. In this case, the composition of the system cannot be