Modern Engineering Thermodynamics

70 CHAPTER 3: Thermodynamic Properties
Several thermodynamic properties have discontinuities at the critical state; β, κ, and c p become infinite there. Near
the critical state, a transparent substance becomes almost opaque due to light scattering caused by large fluctuations
in local density. This phenomenon, called critical opalescence, is illustrated in Figure 3.11. Notice the appearance
of the liquid-vapor interface in Figure 3.11b when the temperature becomes less than the critical temperature.
Table 3.4 Critical State Properties for Various Substances (see also Table C.12)
Substance T c (R) T c (K) p c (psia) p c (MPa) v c (ft 3 /lbm) v c (m 3 /kg)
Ammonia (NH 3 ) 729.9 405.5 1636 11.28 0.068 0.0043
Carbon dioxide (CO 2 ) 547.5 304.2 1071 7.39 0.034 0.0021
Carbon monoxide (CO) 240.0 133.0 507.0 3.50 0.053 0.0033
Helium (He) 9.5 5.3 33.2 0.23 0.231 0.0144
Hydrogen (H 2 ) 59.9 33.3 188.1 1.30 0.516 0.0322
Nitrogen (N 2 ) 227.1 126.2 491.68 3.39 0.051 0.0032
Oxygen (O 2 ) 278.6 154.8 736.9 5.08 0.039 0.0024
Sulfur dioxide (SO 2 ) 775.2 430.7 1143 7.88 0.030 0.0019
Water (H 2 O) 1165.1 647.3 3203.8 22.09 0.051 0.0032
Source: Van Wylen, G. J., Sonntag, R. E., 1986. Fundamentals of Classical Thermodynamics, third ed. Wiley, New York. Reprinted by
permission of John Wiley & Sons.
(a) (b) (c) (d)
FIGURE 3.11
The glass bulb contains carbon dioxide near the critical density ρ critical , and three balls with densities ρ A ≲ ρ critical ρ B = ρ critical , and
ρ C ≳ ρ critical . In (a), the temperature is well above the critical temperature, leaving all the carbon dioxide in the gaseous state. In (b), the
temperature is only slightly above the critical temperature and the carbon dioxide has become foggy. In (c), the temperature is slightly
below the critical temperature and a meniscus has developed separating the gaseous and liquid states. In (d), the temperature is far
below the critical temperature and the density of the liquid has increased to the point where all three balls now float on the surface of
the liquid. (Source: Reprinted with permission from Sengers J. V., Sengers, A. L., 1968. The critical region. Chem. Eng. News 48, 104.)
HOW DO YOU MAKE A DIAMOND?
Diamond is the hardest naturally occurring material known, and it is also the most popular gemstone (Figure 3.12). For
centuries, it has been one of the most desirable and mysterious materials available. In 1772, the French Chemist Antoine-
Laurent Lavoisier (1743–1794) proved that diamond was just another crystalline form of carbon. He invested a