Page 244 - The Mechatronics Handbook

0066_frame_C12 Page 14 Wednesday, January 9, 2002 4:22 PM

When a mixture of liquid and vapor coexists in equilibrium, the liquid phase is a saturated liquid and
the vapor phase is a saturated vapor. The total volume of any such mixture is V = V f + V g ; or, alternatively,
mv = m f v f + m g v g , where m and v denote mass and specific volume, respectively. Dividing by the total
mass of the mixture m and letting the mass fraction of the vapor in the mixture, m g /m, be symbolized
by x, called the quality, the apparent specific volume v of the mixture is

v = ( 1 x)v f + xv g = v f + xv fg (12.16a)
–
where v fg = v g – v f . Expressions similar in form can be written for internal energy, enthalpy, and entropy:

u = ( 1 x)u f + xu g = u f + xu fg (12.16b)
–

h = ( 1 x)h f + xh g = h f + xh fg (12.16c)
–
s = ( 1 x)s f + xs g = s f + xs fg (12.16d)
–

Thermodynamic Data Retrieval
Tabular presentations of pressure, specific volume, and temperature are available for practically important
gases and liquids. The tables normally include other properties useful for thermodynamic analyses, such
as internal energy, enthalpy, and entropy. The various steam tables included in the references of this
chapter provide examples. Computer software for retrieving the properties of a wide range of substances
is also available, as, for example, the ASME Steam Tables (1993) and Bornakke and Sonntag (1996).
Increasingly, textbooks come with computer disks providing thermodynamic property data for water,
certain refrigerants, and several gases modeled as ideal gases—see, e.g., Moran and Shapiro (2000).
The sample steam table data presented in Table 12.3 are representative of data available for substances
commonly encountered in engineering practice. The form of the tables and how they are used are assumed
to be familiar. In particular, the use of linear interpolation with such tables is assumed known.
Specific internal energy, enthalpy, and entropy data are determined relative to arbitrary datums and
such datums vary from substance to substance. Referring to Table 12.3a, the datum state for the specific
internal energy and specific entropy of water is seen to correspond to saturated liquid water at 0.01°C
(32.02°F), the triple point temperature. The value of each of these properties is set to zero at this state.
If calculations are performed involving only differences in a particular specific property, the datum
cancels. When there are changes in chemical composition during the process, special care must be
exercised. The approach followed when composition changes due to chemical reaction is considered in
Moran and Shapiro (2000).
Liquid water data (see Table 12.3d) suggests that at fixed temperature the variation of specific volume,
internal energy, and entropy with pressure is slight. The variation of specific enthalpy with pressure at
fixed temperature is somewhat greater because pressure is explicit in the definition of enthalpy. This
behavior for v, u, s, and h is exhibited generally by liquid data and provides the basis for the following
set of equations for estimating property data at liquid states from saturated liquid data:
vT, p) ≈ v f T() (12.17a)
(

(
uT, p) ≈ u f T() (12.17b)
hT, p) ≈ h f T() + v f pp sat T()] (12.17c)
(
[
–
sT, p) ≈ s f T() (12.17d)
(

©2002 CRC Press LLC