Page 123 - Mechanical Engineers' Handbook (Volume 4)

112 Thermodynamics Fundamentals

system). As the specific volume v decreases, the substance ceases to be a pure vapor at state
g, where the first droplets of liquid are formed. State g is a saturated vapor state.It is
observed that isothermal compression beyond g proceeds at constant pressure up to state ƒ,
where the last bubble (immersed in liquid) is suppressed. State ƒ is a saturated liquid state.
Isothermal compression beyond ƒ is accompanied by a steep rise in pressure, depending on
the compressibility of the liquid phase. The critical state is the intersection of the locus of
saturated vapor states with the locus of saturated liquid states (Fig. 4a). The temperature and
pressure corresponding to the critical state are the critical temperature and critical pressure.
Table 2 contains a compilation of critical-state properties of some of the more common
substances.
Figure 4b shows the projection of the liquid and vapor domain on the T-s plane. On
the same drawing is shown the relative positioning (the relative slopes) of the traces of
various constant-property cuts through the three-dimensional surface on which all the equi-
librium states are positioned. In the two-phase region, the temperature is a unique function
of pressure. This one-to-one relationship is indicated also by the Clapeyron relation
h h ƒ s s ƒ
dP
g
g
dT T(v v ) v v
sat g ƒ g ƒ
where the subscript sat is a reminder that the relation holds for saturated states (such as g
and ƒ) and for mixtures of two saturated phases. Subscripts g and ƒ indicate properties

Table 2 Critical-State Properties 1

Critical Critical Critical Specific
Temperature Pressure Volume
3
Fluid [K ( C)] [MPa (atm)] (cm /g)
Air 133.2 ( 140) 3.77 (37.2) 2.9
Alcohol (methyl) 513.2 (240) 7.98 (78.7) 3.7
Alcohol (ethyl) 516.5 (243.3) 6.39 (63.1) 3.6
Ammonia 405.4 (132.2) 11.3 (111.6) 4.25
Argon 150.9 ( 122.2) 4.86 (48) 1.88
Butane 425.9 (152.8) 3.65 (36) 4.4
Carbon dioxide 304.3 (31.1) 7.4 (73) 2.2
Carbon monoxide 134.3 ( 138.9) 3.54 (35) 3.2
Carbon tetrachloride 555.9 (282.8) 4.56 (45) 1.81
Chlorine 417 (143.9) 7.72 (76.14) 1.75
Ethane 305.4 (32.2) 4.94 (48.8) 4.75
Ethylene 282.6 (9.4) 5.85 (57.7) 4.6
Helium 5.2 ( 268) 0.228 (2.25) 14.4
Hexane 508.2 (235) 2.99 (29.5) 4.25
Hydrogen 33.2 ( 240) 1.30 (12.79) 32.3
Methane 190.9 ( 82.2) 4.64 (45.8) 6.2
Methyl chloride 416.5 (143.3) 6.67 (65.8) 2.7
Neon 44.2 ( 288.9) 2.7 (26.6) 2.1
Nitric oxide 179.2 ( 93.9) 6.58 (65) 1.94
Nitrogen 125.9 ( 147.2) 3.39 (33.5) 3.25
Octane 569.3 (296.1) 2.5 (24.63) 4.25
Oxygen 154.3 ( 118.9) 5.03 (49.7) 2.3
Propane 368.7 (95.6) 4.36 (43) 4.4
Sulfur dioxide 430.4 (157.2) 7.87 (77.7) 1.94
Water 647 (373.9) 22.1 (218.2) 3.1