1. حرارة وديناميكا حرارية
المحاضرة الرابعة
د/ محرز لولو

2. Compressibility Factor is a Measure of Derivation from Ideal-Gas Behavior
Compressibility Factor, Z
Z = Pv/RT
Z = vactual/videal
Ideal gas: Z = 1
Real gases:
Z > 1
Z = 1
Z < 1

3. Real Gases 1 Z T1 T2 T3
T1 < T2 < T3
Ideal Gas P

4. Virial equation of state
We search about a general equation of state: Expand PV/RT in power series From Van der Waal’s equation

5. Compare equation 1,2

6. a, b are van der Waals parameters
Boyle temperature TB
The second virial coefficient B
B = b-(a/RT)
a, b are van der Waals parameters
when B=0
b = a/RT 
TB = (a/bR)
For carbon dioxide
a= 3.59 L2 atm/mol2; b=0.043 L/mol
Boyle temperature TB = 3.59 / (0.043 x 0.082) = 1018 K

7. The reduced equation of state
Define:
Pr is reduced pressure
Vr is the reduced volume
Tr is the reduced temperature

8. The van der Waals equation:
may be expressed in reduced form:
Substituting values for the critical constants in terms of the van der Waals parameters:

9. simplifying:
This expression has the same form as the van der Waals equation, except the van der Waals parameters have disappeared, indicating that the expression does not depend on the identify of the gas.

10. The adiabatic compressibility
We can define

11. The P-V-T surface

12. Properties of Pure Substances

13. Pure Substance
A substance that has a fixed chemical composition throughout is called a Pure Substance.
Pure Substance:
- N2, O2, gaseous Air
-A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous Air is not.

14. Phases of a Pure Substance
Solid
-The molecules in a solid are kept at their positions by the large intermolecular forces.
-The attractive and repulsive forces between the molecules tend to maintain them at relatively constant distances from each other.
Liquid: Groups of molecules move about each other.
Gas: Molecules move about at random.

16. Phase-Change Processes of Pure Substance
Compressed liquid or a subcooled liquid : A liquid that is not about to vaporize.
Saturated liquid: A liquid that is about to vaporize.
Saturated vapor : A vapor that is about to condense.
Saturated liquid-vapor mixture: the liquid and vapor phases coexist in equilibrium.
Superheated vapor: if the vapor is not heated beyond the saturated vapor

17. T-v diagram for the heating process of water at constant pressure.
Saturated
liquid
Saturated
vapor
Once the boiling point is reached, the water’s temperature stays the same until all the water is vaporized. The water goes from a liquid state to a vapor state and receives energy in the form of “latent heat of vaporization”. As long as there’s some liquid water left, the steam’s temperature is the same as the liquid water’s. When all the water is vaporized then we get saturated vapor., any subsequent addition of heat raises the steam’s temperature. Steam heated beyond the saturated steam level is called superheated vapour.

18. Phase-Change Processes of Pure Substance
Saturated temperature, Tsat: At a given pressure, the temperature at which a pure substance changes phase.
Saturated pressure, Psat: At a given temperature, the pressure at which a pure substance changes phase.
Latent heat: the amount of energy absorbed or released during a phase-change process.
Latent heat of fusion: the amount of energy absorbed during melting.
Latent heat of vaporization: the amount of energy absorbed during vaporization.

19. The p-V-T surface for water
Solid in equilibrium with vapor (0 oC)
Solid in equilibrium with vapor and liquid (0 oC)
Liquid and vapor in equilibrium
( 0 < T < 100 oC)
Saturated Vapor (T = 100 oC)
Superheated Vapor (T > 100 oC)

20. Property Diagrams for Phase- Change Processes
The T-v diagram:
-Critical point: the point at which the saturated liquid and saturated vapor states are identical.
The critical-point properties of water : (Pcr= 22.09MPa, Tcr= C, vcr= m3 /kg)

21. Copyright © The McGraw-Hill Companies, Inc
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-16 T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures (numerical values are for water).
2-2

22. FIGURE 3-18 T-v diagram of a pure substance.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-18 T-v diagram of a pure substance.
2-3

23. Property Diagrams for Phase- Change Processes
The P-v diagram:
- The triple line: three phases of a pure substance coexist in equilibrium, these triple-phase states forms a line.
- The triple point: the triple line appears as a point on the P-T diagrams.
-The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium , (For water, 0.01C & kPa)

24. P-v diagram of a substance that expands on freezing (such as water).
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
P-v diagram of a substance that expands on freezing (such as water).
2-6

25. The p-T plane for water, Phase diagram
Liquid
Vapor- Liquid
Critical Point
Vapor
Triple Point p T
Solid

26. Copyright © The McGraw-Hill Companies, Inc
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 3-27 P-v-T surface of a substance that expands on freezing (like water).
2-9

27. The p-V-T surface for ideal gas

28. Equation of state:
Any equation that relates the pressure, temperature, and specific volume of a substance.
Gas: The vapor phase of a substance
Vapor: A gas that is not far from a state of condensation

29. Phase Change
Condensation: gas to liquid
Vaporization liquid to gas
Freezing liquid to solid
Melting (fusion) solid to liquid
Sublimation Solid to gas
Deposition Solid to liquid