4.1 Normal Properties: WATER

Here, we study events of water (as the system) subject to the condition of constant pressure at one atmosphere. The brief phase diagram for water (below right) indicates, as a shaded domain, the normal states of of water. Normal means "having the pressure, one atmosphere."

There are very many industrial events of water that occur at constant atmospheric pressure. Once we learn these cases, extension of technique to other pressures follows without difficulty. Two common data formats for normal properties of water are presented below.

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4.1 Normal Properties: WATER

Here, we study events of water (as the system) subject to the condition of constant pressure at one atmosphere. The brief phase diagram for water (below right) indicates, as a shaded domain, the normal states of of water. Normal means "having the pressure, one atmosphere."

There are very many industrial events of water that occur at constant atmospheric pressure. Once we learn these cases, extension of technique to other pressures follows without difficulty. Two common data formats for normal properties of water are presented below.

Average Specific Heat Data:  Note: for the sake of proper printing, the figure below is moved ahead of its text introduction.

WATER - Average Specific Heats at One Atmosphere
T < 0°C (solid) (T < 32°F)	T = 0°C (solid and/or liquid) (T = 32°F)	0 < T < 100°C (liquid) (32 < T < 212°F)	T = 100°C (liquid and/or gas) (T = 212°F)	T> 100°C (gas) (T> 212 °F)
ρsol 0.92 g/cm3 (57.2 lbm/ft3)	ρsf = ρliq - ρsol 0.08 g/cm3 (5.2 lbm/ft3)	ρliq 1.00 g/cm3 (62.4 lbm/ft3)	vfg = vg - vf 1679 cm3/g (26.8 ft3/lbm)	Ideal Gas
csol 1.96 J/g°C (0.45 Btu/lbm°F)	hsf = hf - hs 333 J/g (144 B/lbm°F)	cliq 4.2 J/g°C (1.00 Btu/lbm°F)	hfg = hg - hf 2252 J/g (970 Btu/lbm)	cp,gas 1.87 J/g°C (99 Btu/lbm°F)

Average Specific Heat Data:  The upper panel (above table)shows a perspective view of the p-v-T surface for the pressure-wise slice, "normal properties." The image has temperature as its abscissa (temperature, the horizontal axis, - increases to the right). Beneath the graphic, the tabled numerical data have the same temperature orientation but with some being temperature ranges (as T < 0°C) or otherwise being a precise temperature (t = 0°C). The graphic and tabular data respect the temperature axis.

Data of the left-most column, are seen by row one to apply to solid water with temperatures less the than 0°C. The second row and third row of that column present representative values for density and specific heat of the solid respectively. The first, third, and fifth column (for solid, liquid and gas respectively) contain analogous data. The second column applies to water precisely 0°C. The data of its rows two and three present "latent," or solid - liquid, phase change information. Data for T = 100°C are also called "latent." Our uses of these data in examples will help make them clear.

Upon careful inspection of the section of the p-v-T surface (with the phase diagram in comparison), one can see that at precisely freezing, 0°C (0^-°C < 0°C < 0⁺°C) a a "point" on the surface section is not established by intersection of the lines, T = 0°C and p = 1 atm. The intersection appears to indicate a "short line" when, in fact the intersection is two points. One point is very close to the point, 1 atm and 0°⁺C. The other point is close to 1 atm and 0°^-C. There are only pseudo states on the line that connects these points. This also the case, by similar argument, for the point, 1 atm, 100°C. The notation " 0⁺°C " means a temperature very slightly greater than 0°C (0^-°C means a temperature very slightly less than 0°C).

Tabular Data:   Tabular data for water occupy literally pages of thermodynamics texts. Here in introduction to properties, we have extracted a single set of data in table format. The pressure is one atmosphere (101.3 kPa) and the temperature range is -40°C to 500°C with the data of two phase change increments included. Properties of water are discontinuous upon freezing (or melting) and upon boiling (or condensing). For ease of learning a special notation is used to include these phase change data in the table.

Water at One Atmosphere
p (Ts(p))		-40°C	0-°C	0+°C	100-°C	100+°C	500°C
101.3 kPa (100)oC	v  u  h	1.08 -410 -411	1.09 -332 -333	1.00 0.10 0.10	1.04 418 419	1680 2505 2675	3534 3130 3488
v ~ cm3/g     u ~ J/g      h ~ J/g

Temperatures, least to greatest are: 0^-oC < 0^oC < 0^+oC. Freezing of water occurs at 0^oC. About solid water at 0^-oC, one might say, depending upon temperature change, "the water has just completed freezing" or "it is about to commence melting." The state associated with the temperature 0^+oC is liquid water that temperature-wise has either "just completed melting" or "is about to freeze." Vaporization and condensing occur at 100^oC and a similar description of phase change can be made. All descriptions are awkward. In freezing any practical amount of water there is not first liquid then solid. There is liquid, then a little solid and liquid, then more solid and less liquid... and finally all solid. Phase change intensive properties do not proceed through states but rather proportions of states notated "+" and "-," which are called saturation states. Better to do than to talk!

Tabular data are convenient in that specific heats and latent heats are "built in." A disadvantage is tabular data is discrete. In their use, interpolation is frequently required. Manners and techniques of use of these data will be explained in the context of examples.