Introd to chem eng Thermodynamics-2

FORMULATION OF THE FIRST LAW OF THERMODYNAMICS
THE THERMODYNAMIC STATE AND STATE FUNCTIONS
THE STEADY-STATE FLOW PROCESS
EQUILIBRIUM
THE PHASE RULE
THE REVERSIBLE PROCESS
THE PVT BEHAVIOR OF PURE SUBSTANCES
Thermodynamic properties, such as internal energy and enthalpy, from which
one calculates the heat and work requirements of industrial processes, are not
directly measurable. They can, however, be calculated from volumetric data. To
provide part of the background for such calculations, we describe in this chapter
the pressure-volume-temperature (PIT) behavior of pure fluids. Moreover, these
PIT relations are important in themselves for such purposes as the metering of
fluids and the sizing of vessels and pipelines.
Homogeneous fluids are normally divided into two classes, liquids and gases.
However, the distinction cannot always be sharply drawn, because the two phases
become indistinguishable at what is called the critical point. Measurements of the
vapor pressure of a pure solid at temperatures up to its triple point and measurements
of the vapor pressure of the pure liquid at temperatures above the triple
point lead to a pressure-vs.-temperature curve such as the one made up of lines
1-2 and 2-C in Fig. 3.1. The third line (2-3) shown on this graph gives the
solid/liquid equilibrium relationship. These three curves represent the conditions
of P and T required for the coexistence of two phases and thus are boundaries
for the single-phase regions. Line 1-2, the sublimation curve, separates the solid
and gas regions; line 2-3, the fusion curve, separates the solid and liquid regions;
line 2-C, the vaporization curve, separates the liquid and gas regions. The three
curves meet at the triple point, where all three phases coexist in equilibrium.
According to the phase rule [Eq. (2.12)], the triple point is invariant. If the system
exists along any of the two-phase lines of Fig. 3.1, it is univariant, whereas in
the single-phase regions it is divariant. Although the fusion curve 2-3 continues
upward indefinitely, the vaporization curve 2-C terminates at point C, the critical
point. The coordinates of this point are the critical pressure P, and the critical
temperature T" the highest temperature and pressure at which a pure material
can exist in vapor/liquid equilibrium. The fluid region, existing at higher temperatures
and pressures, is marked of! by dashed lines, which do not represent
phase transitions, but rather are limits fixed by the meanings accorded the words
liquid and gas. A phase is generally considered a liquid if it can be vaporized
by reduction in pressure at constant temperature. A phase is considered a gas if
it can be condensed by reduction of temperature at constant pressure. Since the
Ouid region fits neither of these definitions, it is neither a gas nor a liquid. The
gas region is sometimes divided into two parts, as shown by the dotted line of
Fig. 3.1. A gas to the left of this line, which can be condensed either by compression
at constant temperature or by cooling at constant pressure, is called a vapor.
Because of the existence of the critical point, a path can be drawn from the
liquid region to the gas region that does not cross a phase boundary; e.g., the
path from A to B in Fig. 3.1. This path represents a gradual transition from the
liquid to the gas region. On the other hand, a path crossing phase boundary 2-C
includes a vaporization step, where an abrupt change of properties OCCurs.
Figure 3.1 does not provide any information about volume; it merely displays
the phase boundaries on a PT diagram. Consider now a series of isotherms,
vertical lines on Fig. 3.1 lying to the right of the solid region, and a plot of
pressure vs. molar or specific volume for each isotherm. The PV diagram which
results is sketched in Fig. 3.2. The lines labeled T, and T2 are isotherms at
temperatures greater than the critical. As seen from Fig. 3.1, such isotherms do
not cross a phase boundary and are therefore smooth. The lines labeled T, and
T. are for lower temperatures and consist of three distinct sections. The horizontal
sections represent the phase change between vapor and liquid. The constant
pressure at which this occurs for a given temperature is the vapor pressure, and
is given by the point on Fig. 3.1 where the isotherm crosses the vaporization
curve. Points along the horizontal lines of Fig. 3.2 represent all possible mixtures
of vapor and liquid in equilibrium, ranging from 100 percent liquid at the left
end to 100 percent vapor at the right end. The locus of these end points is the
dome-shaped curve labeled ACB, the left half of which (from A to C) represents
saturated liquid, and the right half (from C to B) saturated vapor. The area under
the dome ACB is the two-phase region, while the areas to the left and right are
the liquid and gas regions. The isotherms in the liquid region are very steep,
because liquid volumes change little with large changes in pressure.
The horizontal segments of the isotherms in the two-phase region become
progressively shorter at higher temperatures, being ultimately reduced to a point
at C. Thus, the critical isotherm, labeled Tn exhibits a horizontal inflection at
the critical point C at the top of the dome. Here the liquid and vapor phases
cannot be distinguished from one another, because their properties are the same.
The physical significance of the critical point becomes evident from the
changes that occur when a pure substance is heated in a sealed upright tube of
constant volume. Such changes follow vertical lines in Fig. 3.2. They are also
shown on the PT diagram of Fig. 3.3, where the vaporiiation curve of Fig. 3.1
appears as a solid line. The dashed lines are constant-volume paths in the
single-phase regions only. If the tube is filled with either liquid or gas, the heating
process produces changes described by these lines, for example by the change
from D to E (liquid region) and by the change from F to G (vapor region). The
corresponding vertical lines on Fig. 3.2 lie to the left and to the right of ACB.
If the tube is only partially filled with liquid (the remainder being vapor in
equilibrium with the liquid), heating at first causes changes described by the
vapor-pressure curve (solid line) of Fig. 3.3. If the meniscus separating the two
phases is initially near the bottom of the tube, liquid vaporizes, and the meniscus
recedes to the bottom of the tube and disappears as the last drop of liquid
vaporizes. For example in Fig. 3.3, one such path is from (1, K) to N; it then
fOllows the line of constant molar volume V2 upon further heating. If the meniscus
is originally near the top of the tube, the liquid expands upon heating until it
completely fills the tube. One such process is represented by the path from (1, K)
to P; it then follows the line of constant molar volume Vi with continued heating.
The two paths are also shown by the dashed lines of Fig. 3.2, the first passing
through points K and N, and the second through J and P.
A unique filling of the tube, with a particular intermediate meniscus level,
causes the path of the heating process to coincide with the vapor-pressure curve
of Fig. 3.3 all the way to its end at the critical point C. On Fig. 3.2 the path is a
vertical line passing through the critical point. Physically, heating does not
produce much change in the level of the meniscus. As the critical point is
approached, the meniscus becomes indistinct, then hazy, and finally disappears
as the system changes from two phases (as represented by the vapor-pressure
curve) to a single phase (as represented by the region above C). Further heating