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ME1521 Properties of Pure Substances Reading: Cengel & Boles, Chapter 2
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ME1522 Liquid & Vapor Phases of a Pure Substance Compressed (subcooled) liquid Saturated liquid Saturated liquid-vapor mixture Saturated vapor Superheated vapor
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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
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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
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ME1525 New Properties Enthalpy - property of “convenience”, primarily used in control volume analysis Quality - intensive property used to describe saturated, liquid-vapor states
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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):
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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
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ME1528 Property Tables (Cengel & Boles) Table A-1: molecular weight (M), critical properties (T cr, P cr ) Phase tables:
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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
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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
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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 8.314 kJ/kmol-K
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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:
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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
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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!)
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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:
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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
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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
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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
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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
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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
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ME15221 Specific Heat Relations For ideal gases, Differentiating wrt T, Define specific heat ratio, k :
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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
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ME15223 Specific Heats of Incom- pressible Substances, cont. Enthalpy change, For constant pressure processes, For constant temperature processes,
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