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.

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).

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).

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)

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).

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

Vapor-liquid phase equilibrium in a pure substance

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

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.

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.

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)

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.

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 = 1+2-1 = 2 (simple thermodynamic system) Two phase, single-phase component (such as saturated liquid or saturated vapor): F = 1+2-2 = 1 For pure saturated liquid or vapor only. However, for a two-phase mixture, need quality x still, two variables.

Equation of State for an Ideal Gas

Equation of State for an Ideal Gas

Equation of State for a Gas

Equation of State for a Gas or Vapor

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.

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

Enthalpy-a derived thermodynamic property

The constant-volume/constant-pressure specific heats

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.

The constant-volume/constant-pressure specific heats

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.

The constant-volume/constant-pressure specific heats

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.