(even a mixture of ice and water is pure)
PURE SUBSTANCE: Fixed chemical composition, throughout H2O, N2, CO2, Air
COMPRESSED LIQUID: NOT about to vaporize
(Sub-cooed liquid) e.g., water at 20oC and 1 atmosphere
SATURATED LIQUID: about to vaporize
e.g., water at 100oC and 1 atmosphere
SATURATED VAPOR: about to condense
e.g., water vapor (steam) at 100oC and 1 atm.
SUPERHEATED VAPOR: NOT about to condense
e.g., water vapor (steam) at >100oC and 1 atm.
Tv Diagram for Heating H2O at Constant Pressure (Figure 2-11):
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
Liquid-Vapor Saturation Curve for Water (Figure 2-12):
useful in studying and understanding phase change processes.
For water (Figure 2-13):
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 A-1:
- PCR = 22.09 MPa
- TCR = 374.14 oC (or 647.3 oK)
- vCR = 0.003155 m3/kg (or .0568 m3/kmol)
MORE T-v DIAGRAMS (Figure 2-15):
P-v DIAGRAMS (Figure 2-16): Note: Constant Temperature lines go downward.
P-T DIAGRAM (Figure 2-22): Shows the TRIPLE POINT
|The ONLY point where all 3 phases (solid, liquid, and
vapor) can exist in equilibrium
The triple point for H2O:
vf = specific volume of the saturated LIQUID
vg = specific volume of the saturated VAPOR
vfg = the difference between the specific volume of the saturated vapor and saturated liquid = (vg - vf)
LOOK in Table A-4
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
mt vavg = mf vf + mg vg
mf = mt - mg
<-- dividing by the total mass and
applying the definition of Quality, x
vavg = (1 - x) vf + x vg = vf - x vf + x vg = vf + x (-vf + vg) vavg = vf + x vfg
Also, x = (vavg - vf) /vfg
(a common way to evaluate the quality)
Quality is used to find other properties of saturated liquid-vapor mixtures (Fig. 2-32):
GIVEN: 0.05 kg of water at 25oC in a container of 1.0 m3 volume.
FIND: the phase description, pressure, and quality (if appropriate).
WHY might the quality be inappropriate ???
Find the proper table: Water + given T, use Table A-4
Look up vf = 0.001003 m3/kg vg = 43.36 m3/kg
Calculate v (= vavg) = V/m = 1.0 m3/0.05 kg = 20 m3/kg
Since vf < vavg < vg the phase is saturated liquid-vapor mixture
Since this is a saturated state: P = P
no longer any liquid, NOT about to condense.
at a given P, T > TSAT or
at a given T, P < PSAT or
at either a given P or T, v > vg or h > hg or u > ug
Evaluate the properties of superheated water in Table A-6
Table A-6 has a different format than saturated data tables (A-4 and A-5), because P and T are now independent i.e., for a given pressure, a series of temperatures are tabulated
Water at P = 0.5 MPa, h = 2890 kJ/kg. Find T.
Check Table A-5 (given P) finding hg = 2748.7 kJ/kg
since h > hg, this is a superheated vapor !
From Table A-6 at P = 0.5 MPa, find two rows that bracket the given h
|Temperature (oC)||Enthalpy (kJ/kg)||
h of 2890 kJ/kg is between these values
Make your own Interpolation Table:
|Temperature (oC)||Enthalpy (kJ/kg)|
no vapor, all liquid, NOT about to vaporize
at a given P, T < TSAT or
at a given T, P > PSAT or
at either a given P or T, v < vf or h < hf or u < uf
Usually we approximate compressed liquid behavior (Figure 2-33) evaluated at the given TEMPERATURE (dont use the pressure)
v = vf@T
h = hf@T
u = uf@T
Before we leave this section, look at Tables A-8, A-9, A-10.
This data is for Refrigerant 134a, commonly used in air conditioning systems. You have the same tables: Saturated liquid-vapor mixtures (both a temperature and pressure table), and the superheated vapor table.
Problems with R-134a 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 PR << 1||
|(PR = P/PCR)|
|2)||at high temperatures,||if TR > 2||
unless PR >> 1
|(TR = T/TCR)|
The gas constant, R = Ru/M
where: Ru = the universal gas constant
Ru = 8.314 kJ/kmole-K (for all gases)
M = the molecular weight of the gas (kg/kmole ) Table A-1
P V = N Ru 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
P v = R T gives (kPa) (m3/kg) = (kJ/kg-oK) (oK)
Notice: 1 kJ = 1 kPa-m3
For changes of state (with a fixed mass of Ideal gas):
P1 v1 = R T1 and P2 v2 = R T2
(P1 v1)/T1 = R and (P2 v2)/T2 = R
(P1 v1)/T1 = (P2 v2)/T2
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 = (vACTUAL)/(vIDEAL)
Z is found in the charts in Figure 2-40 and Appendix A-13, using the quantities:
PR (Reduced Pressure) = P/PCRITICAL
TR (Reduced Temperature) = T/TCRITICAL
vR ("Reduced" Specific Vol.)
= vACTUAL PCR / (R TCR)
The Compressibility charts can be used for ALL GASES.
EXAMPLE: Air at 164oK, 10.17 MPa. What is Z ??
Table A-1: Find TCR and PCR for AIR
TCR = 132.5oK and PCR = 3.77 MPa
TR = T / TCR = 164oK / 132.5oK = 1.24
PR = P / PCR = 10.17 MPa / 3.77 MPa = 2.7
Use Figure 2-40, READ Z from the graph.
Also notice, in Fig A-13, you can also read vR from the graph
(have more terms - applicable in larger range of TR and PR, see Fig. 2-48)
Van der Waals (2 constants): (P + a/v2)(v - b) = R T
Beattie-Bridgeman (5 constants)
Benedict-Webb-Rubin (8 constants)
Strobridge (16 constants)
Virial (power series form)