METBD 330: Thermodynamics

Chapter 2:

PURE SUBSTANCE:  Fixed chemical composition, throughout H2O, N2, CO2, Air  (even a mixture of ice and water is pure)

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):

Fig2_11.gif (4835 bytes)

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):

Fig2_12.gif (4163 bytes)

T-v Diagrams: useful in studying and understanding phase change processes.

For water (Figure 2-13):

Fig2_13.gif (5808 bytes)


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:

for H2O:

  • 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):

Fig2_15.gif (5438 bytes)

P-v DIAGRAMS (Figure 2-16):  Note: Constant Temperature lines go downward.

Fig2_16.gif (5377 bytes)

P-T DIAGRAM (Figure 2-22):  Shows the TRIPLE POINT

Fig2_22.gif (4359 bytes) The ONLY point where all 3 phases (solid, liquid, and vapor) can exist in equilibrium

The triple point for H2O: 

T = 0.01oC
P = 0.6113 kPa
  (0.6% of 1 atm)





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)

Fig2_3x.gif (4765 bytes)

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.

Fig2_3y.gif (5525 bytes)

QUALITY is defined:

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.

    Test for Ideal Gas behavior (p. 62):

          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


    NON-IDEAL Gas Behavior: Compressibility Factor

    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)