ME1521 Properties of Pure Substances Reading: Cengel & Boles, Chapter 2

ME1522 Liquid & Vapor Phases of a Pure Substance Compressed (subcooled) liquid Saturated liquid Saturated liquid-vapor mixture Saturated vapor Superheated vapor

ME1523 Saturation Pressure & Temperature “Saturation” refers to phase change, typically liquid-vapor The saturation temperature, T sat, is the boiling point at a specified pressure The saturation pressure, P sat, is the pressure at the boiling point Saturation temperature and pressure are dependent properties The latent heat of vaporization is the energy absorbed during vaporization or released during condensation

ME1524 Thermodynamic Properties Pressure, P Temperature, T Volume, V –specific volume, v = V/m Internal energy, U –specific internal energy, u = U/m Enthalpy, H –specific enthalpy, h = H/m Entropy, S –specific entropy, s = S/m Quality, x

ME1525 New Properties Enthalpy - property of “convenience”, primarily used in control volume analysis Quality - intensive property used to describe saturated, liquid-vapor states

ME1526 New Properties, cont. Quality is used to describe saturated states only –Saturated liquid: x = 0 –Saturated liquid-vapor mixture: 0< x <1 –Saturated vapor: x = 1 Quality-property relationships (where y = v, u, h, or s):

ME1527 Thermodynamic Property Data Based upon expt’l measurements Compiled in tables, graphs, and computer software Text tables (Cengel & Boles) –SI units: A-1 to A-29 –(English units: A-1E to A-29E) –H 2 O properties: A-4 to A-8 –R-134a properties: A-11 to A-13 –Selected solid & liquid properties: A-3 –Ideal gas properties: A-2, A-17 to A-25 –Thermochemical properties: A-26 to A-28

ME1528 Property Tables (Cengel & Boles) Table A-1: molecular weight (M), critical properties (T cr, P cr ) Phase tables:

ME1529 Compressed Liquid Properties Compressed liquid property tables are usually not available because these properties are relatively independent of pressure General approximation for v, u, h, and s as a compressed liquid: The approximation for h at higher pressures can be improved using

ME15210 The State Postulate General rule for determining the number of independent, intensive properties needed to specify a state of a system: N = 1 + [no. of work interactions] Simple, Compressible System – refers to system with only one type of work interaction – compression- expansion work – therefore, only two independent, intensive properties are needed to specify a state

ME15211 The Ideal Gas Equation of State Equation of state - any equation that relates P, v, and T Gas - a superheated vapor, usually where T > T cr Experiments with gases show that This constant is known as the universal gas constant, R u, which has a value of kJ/kmol-K

ME15212 The Ideal Gas Equation of State, cont. The resulting equation is often called the ideal gas law, written as where R is the gas constant and M is the molecular weight (mass): Other forms:

ME15213 The Ideal Gas Equation of State, cont. For closed system analysis (m = constant), the PV=mRT form is very useful: –where 1 and 2 refer to the gas properties at two different states

ME15214 When is the Ideal Gas Equation of State Valid? Can be used for light gases such as air, N 2, O 2, H 2, He, Ar, Ne, Kr, and CO 2 at relatively low pressure or high temperature: The ideal gas law is generally not valid for water vapor in steam power plants or refrigerant vapors in refrigeration or heat pump systems (use property tables for these!)

ME15215 The Compressibility Factor The deviation from ideal gas behavior is quantified by the compressibility factor, Z : Z = 1 is an ideal gas; real gases may have Z 1 The generalized compressibility chart (see Figures A-30a,b,c) allows evaluation of Z using a reduced pressure and reduced temperature:

ME15216 Specific Heat Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree The required energy depends upon how the process is executed: –constant volume –constant pressure

ME15217 Specific Heat, cont. Specific heats (C v, C p ) are properties and do not depend upon the process C p  C v because additional energy must be supplied for the work performed that allows the system to expand at constant pressure Specific heat for a particular substance can change with temperature and pressure

ME15218 Specific Heats of Ideal Gases Experiments show that u = u(T) and h = h(T) for ideal gases; therefore: Separating variables and integrating yields We need C v (T) and C p (T) to carry out these integrations

ME15219 Specific Heats of Ideal Gases, cont. There are three approaches to evaluating u 2 -u 1 and h 2 -h 1 : –using tabulated u and h data (Tables A- 17 to A-25); easiest and most accurate –using polynomial relations for C v and C p as a function of T (Table A-2c) and integrating; accurate but tedious –using a constant specific heat at the average temperature (Table A-2b); simple and reasonably accurate; very convenient when u, h tables are not available

ME15220 Constant Specific Heat Approach Integrations yield: –where the average specific heats are evaluated from Table A-2b at the average temperature (T 1 +T 2 )/2 This approach is exact for monatomic gases such as He, Ne, and Ar because their specific heats are independent of temperature

ME15221 Specific Heat Relations For ideal gases, Differentiating wrt T, Define specific heat ratio, k :

ME15222 Specific Heats of Incom- pressible Substances Solids and liquids are considered incompressible substances Since volume remains constant for incompressible substances, Since u = u(T) for incompressible substances, we have –where C av is found in Table A-3 for solids and liquids at the average temperature (T 1 +T 2 )/2

ME15223 Specific Heats of Incom- pressible Substances, cont. Enthalpy change, For constant pressure processes, For constant temperature processes,