Chapter 2:
PURE SUBSTANCE: Fixed chemical composition, throughout H_{2}O, N_{2}, CO_{2}, Air (even a mixture of ice and water is pure)
COMPRESSED LIQUID: NOT about to vaporize
(Subcooed liquid) e.g., water at 20^{o}C and 1 atmosphere
SATURATED LIQUID: about to vaporize
e.g., water at 100^{o}C and 1 atmosphere
SATURATED VAPOR: about to condense
e.g., water vapor (steam) at 100^{o}C and 1 atm.
SUPERHEATED VAPOR: NOT about to condense
e.g., water vapor (steam) at >100^{o}C and 1 atm.
Tv Diagram for Heating H_{2}O at Constant Pressure (Figure 211):
Pressure Cooker example: the boiling temperature varies with pressure
Saturation Temperature: the boiling temperature at a given pressure
Saturation Pressure: the pressure at which boiling occurs at a given T
LiquidVapor Saturation Curve for Water (Figure 212):
Tv Diagrams: useful in studying and understanding phase change processes.
For water (Figure 213):
CRITICAL POINT:
the saturated liquid and saturated vapor states are identical
No saturated mixture exists  the substance changes directly from the liquid to vapor states.
LOOK at Table A1:
for H_{2}O:
 P_{CR} = 22.09 MPa
 T_{CR} = 374.14 ^{o}C (or 647.3 ^{o}K)
 v_{CR} = 0.003155 m^{3}/kg (or .0568 m^{3}/kmol)
MORE Tv DIAGRAMS (Figure 215):
Pv DIAGRAMS (Figure 216): Note: Constant Temperature lines go downward.
PT DIAGRAM (Figure 222): Shows the TRIPLE POINT
The ONLY point where all 3 phases (solid, liquid, and
vapor) can exist in equilibrium The triple point for H_{2}O:

ENTHALPY, H
PROPERTY TABLES
v_{f} = specific volume of the saturated LIQUID
v_{g} = specific volume of the saturated VAPOR
v_{fg} = the difference between the specific volume of the saturated vapor and saturated liquid = (v_{g}  v_{f})
LOOK in Table A4 ……
Also, in this table:
Find the properties of a mixture using the QUALITY. QUALITY defines the proportions of the liquid and vapor phases in the mixture. 
QUALITY is defined:
QUALITY, x, is never used to describe compressed liquid or superheated vapor !!
Quality may be expressed as a percentage: from 0% to 100%, where 0% is a saturated liquid and 100% is a saturated vapor.
is treated as
m_{t} v_{avg} = m_{f} v_{f} + m_{g }v_{g} m_{f} = m_{t}  m_{g }
< dividing by the total mass and
applying the definition of Quality, xv_{avg} = (1  x) v_{f} + x_{ }v_{g} = v_{f}  x v_{f} + x v_{g } = v_{f} + x (v_{f} + v_{g}) v_{avg} = v_{f} + x v_{fg} Also, x = (v_{avg}  v_{f}) /v_{fg}
(a common way to evaluate the quality) _{ }
Quality is used to find other properties of saturated liquidvapor mixtures (Fig. 232):


GIVEN: 0.05 kg of water at 25^{o}C in a container of 1.0 m^{3} volume.
FIND: the phase description, pressure, and quality (if appropriate).
WHY might the quality be inappropriate ???
Procedure:
Find the proper table: Water + given T, use Table A4
Look up v_{f} = 0.001003 m^{3}/kg v_{g} = 43.36 m^{3}/kg
Calculate v (= v_{avg}) = V/m = 1.0 m^{3}/0.05 kg = 20 m^{3}/kg
Since v_{f} < v_{avg} < v_{g} the phase is saturated liquidvapor mixture
Since this is a saturated state: P = P_{ sat@25C} = 3.169 kPa
SUPERHEATED VAPOR:
no longer any liquid, NOT about to condense.
characteristics:
at a given P, T > T_{SAT} or
at a given T, P < P_{SAT} or
at either a given P or T, v > v_{g} or h > h_{g} or u > u_{g}
Evaluate the properties of superheated water in Table A6
Table A6 has a different format than saturated data tables (A4 and A5), because P and T are now independent i.e., for a given pressure, a series of temperatures are tabulated
EXAMPLE 27
Water at P = 0.5 MPa, h = 2890 kJ/kg. Find T.
Check Table A5 (given P) finding h_{g} = 2748.7 kJ/kg
since h > h_{g}, this is a superheated vapor !
From Table A6 at P = 0.5 MPa, find two rows that bracket the given h
Temperature (^{o}C)  Enthalpy (kJ/kg)  h of 2890 kJ/kg is between these values 
200  2855.4  
250  2960.7 
Make your own Interpolation Table:
Temperature (^{o}C)  Enthalpy (kJ/kg) 
200 
2855.4 
T  2890 
250  2960.7 
COMPRESSED LIQUID:
no vapor, all liquid, NOT about to vaporize
characteristics:
at a given P, T < T_{SAT} or
at a given T, P > P_{SAT} or
at either a given P or T, v < v_{f} or h < h_{f} or u < u_{f}
Usually we approximate compressed liquid behavior (Figure 233) evaluated at the given TEMPERATURE (don’t use the pressure)
v = v_{f@T}
h = h_{f@T}
u = u_{f@T}
Before we leave this section, look at Tables A8, A9, A10.
This data is for Refrigerant 134a, commonly used in air conditioning systems. You have the same tables: Saturated liquidvapor mixtures (both a temperature and pressure table), and the superheated vapor table.
Problems with R134a can be treated using the tables just like problems with water or steam.
The Ideal Gas Equation is: P v = R T
Alternative to using Tables
Defines the state of a gas by relating T, P, and v
R is the gas constant for the specific gas being analyzed
T is the absolute temperature
P is the absolute pressure
P v = R T is valid for gases with low density (r). Low density is found when pressure is low and/or temperature is high.
The gas is:  
1)  at any temperature,  if P_{R} << 1  IDEAL 
(P_{R} = P/P_{CR}) 
2)  at high temperatures,  if T_{R} > 2  IDEAL unless P_{R} >> 1 
(T_{R} = T/T_{CR}) 
The gas constant, R = R_{u}/M
where: R_{u} = the universal gas constant
R_{u} = 8.314 kJ/kmoleK (for all gases)
M = the molecular weight of the gas (kg/kmole ) Table A1
P V = N R_{u} T
uses N, the number of moles of the gas molecules
also, since V = m v, P V = m R T where m is the mass
UNITS:
P v = R T gives (kPa) (m^{3}/kg) = (kJ/kg^{o}K) (^{o}K)
Notice: 1 kJ = 1 kPam^{3}
For changes of state (with a fixed mass of Ideal gas):
P_{1} v_{1} = R T_{1} and P_{2} v_{2} = R T_{2}
(P_{1} v_{1})/T_{1} = R and (P_{2} v_{2})/T_{2} = R
(P_{1} v_{1})/T_{1} = (P_{2} v_{2})/T_{2}
Can you use the Ideal Gas Law for water vapor ????
Almost NEVER, only at very low pressures, < 10 kPa
P v = Z R T
where Z = compressibility factor for gases which are not quite IDEAL
Z is the ratio of the ACTUAL specific volume to the IDEAL specific volume of the gas
Z = (v_{ACTUAL})/(v_{IDEAL})
Z is found in the charts in Figure 240 and Appendix A13, using the quantities:
P_{R} (Reduced Pressure) = P/P_{CRITICAL}
T_{R} (Reduced Temperature) = T/T_{CRITICAL}
v_{R} ("Reduced" Specific Vol.)
= v_{ACTUAL} P_{CR }/ (R T_{CR})
The Compressibility charts can be used for ALL GASES.
EXAMPLE: Air at 164^{o}K, 10.17 MPa. What is Z ??
Table A1: Find T_{CR} and P_{CR} for AIR …
T_{CR} = 132.5^{o}K and P_{CR} = 3.77 MPa
T_{R} = T / T_{CR} = 164^{o}K / 132.5^{o}K = 1.24
P_{R} = P / P_{CR} = 10.17 MPa / 3.77 MPa = 2.7
Use Figure 240, READ Z from the graph.
Also notice, in Fig A13, you can also read v_{R} from the graph_{}
(have more terms  applicable in larger range of T_{R} and P_{R}, see Fig. 248)
Van der Waals (2 constants): (P + a/v^{2})(v  b) = R T
BeattieBridgeman (5 constants)
BenedictWebbRubin (8 constants)
Strobridge (16 constants)
Virial (power series form)