1. Chapter 3: Evaluating Properties
In the previous chapters, we discussed various properties:
v, p, T
Objectives: To evaluate the values of these properties and their
relationship; and the values of these properties in different phases.
Limitations: Consider pure substance only.
Pure substance: A substance that has homogeneous and invariable chemical composition. It may exist in more than one phase, but the chemical composition is the same.
• Liquid water, vapor (steam), ice ~ pure substance, a mixture
of ice and water, a mixture of water and steam.
• Pure substance: every phase has the same chemical composition.

2. Chapter 3: Evaluating Properties
Air is composed of 20.95% O2, 78.08% N2 by volume with some argon and water vapor. Not a pure substance.
However, if the averaged properties based on different chemical components are used, air can be considered to be a pure substance, as long as there is no change of phase.
How properties for pure substances are found?
Experimental measurement. ~ hold some variables while changing one variable (For example in a constant p
process, find relation between T and V).

3. Chapter 3: Evaluating Properties
Since properties are defined based on equilibrium state,
properties should be measured based on equilibrium process.
Different thermal processes are considered, and various
thermal properties are measured during these processes (v, p, T - these are the fundamental properties that could be
directly measured. Other properties such as U may be obtained through the first law of thermodynamics).

4. Vapor-liquid phase equilibrium in a pure substance
a: pure liquid
b: liquid/vapor mixture
c: pure vapor
Saturated vapor
Superheated vapor
Liquid
Saturated Liquid
p = Const
A-B: Subcooled liquid
B-C: Saturated liquid/vapor two-phase
C-D: Superheated vapor
(b)
(c)
Saturated T at a given p
(a)

5. Vapor-liquid phase equilibrium in a pure substance
Saturated T at different p
The test above is repeated at different p (different weights above the piston).

6. Vapor-liquid phase equilibrium in a pure substance
The transition point B is saturated pure liquid or saturated liquid
The transition point C is saturated pure vapor or saturated vapor

7. Vapor-liquid phase equilibrium in a pure substance

8. T-V diagram for water at different pressure
The process for curve A-B- C-D is repeated at different p. The two phase region is shrinking at higher p. B
A: The initial state
B: The saturated liquid state
AB: The liquid is heated from the initial T to the saturation T
C: The saturated vapor state
BC: Constant T (P) process in which the change of phase from
liquid to vapor occurs - two phase (equilibrium) mixture
CD: The process in which the steam is superheated at constant p
N: Critical point, liquid & vapor states are identical

9. Evaluation of extensive properties of a two-phase mixturee
The above relation is for extensive properties associated with the mass of the system. For intensive properties that are independent upon the mass of the system, the above equation is NOT used.

10. Some critical point data
The phase of a substance may be determined by using the data in the above table in conjunction with Fig. 3.2 of the following slide.

11. 3-D Surfaces and two-dimensional projections of the surfaces
In addition to the liquid-vapor two-phase coexisting state, solid-liquid (such as ice-water) and solid-vapor may also co-exist (sublimation: solid phase to the gaseous phase without passing through an intermediate liquid phase). Also see triple line (Fig. 3.2c)

12. Supercritical Fluids (Google)
Carbon dioxide pressure-temperature phase diagram
Water pressure-temperature phase diagram
A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist.

13. Independent properties of pure substance for simple compressible system (in the absence of motion, gravity, and surface, magnetic, or electrical effects)
Independent variables, Gibbs phase rule:
F=C+2-P
P: Number of phase making up a system
F: Degree of freedom (number of independent variables)
C: Number of components in a system
Single phase, single component:
F = = 2 (simple thermodynamic system)
Two phase, single-phase component (such as saturated liquid or saturated vapor):
F = = 1
For pure saturated liquid or vapor only. However, for a two-phase
mixture, need quality x still, two variables.

14. Equation of State for an Ideal Gas

15. Equation of State for an Ideal Gas

16. Equation of State for a Gas

17. Equation of State for a Gas or Vapor

18. Equation of State for a gas or vapor
At a temperature around 300 K and a pressure below 10 MPa, most gases can be treated as an ideal gas.

19. Enthalpy-a derived thermodynamic property
Let us consider a control mass undergoing a quasi-equilibrium constant-pressure process.
H = U + pV

20. Enthalpy-a derived thermodynamic property

21. The constant-volume/constant-pressure specific heats

22. The constant-volume/constant-pressure specific heats
The definition of a specific heat is based on a specific process, either constant volume or constant pressure process. However, once it is defined and found to be a property, it can be used for any processes.

23. The constant-volume/constant-pressure specific heats

24. The constant-volume/constant-pressure specific heats
The derivations of du = cv dT and dh = cp dT are respectively based on a constant volume and a constant pressure process, but they are applicable to any processes, not just constant volume or constant pressure process.

25. The constant-volume/constant-pressure specific heats

26. Evaluate h and u of an ideal gas
Integrate the above equation between T1 and T2.
The value of hT can be tabulated in an ideal gas table. The use of an ideal gas table is accurate and convenient.