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Properties of Pure Substances. Property Diagrams for Phase-Change Processes. To understand what happens during phase change process, display the relationship of properties on diagrams: Temperature-specific volume Pressure-specific volume Pressure-Temperature.
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Property Diagrams for Phase-Change Processes • To understand what happens during phase change process, display the relationship of properties on diagrams: • Temperature-specific volume • Pressure-specific volume • Pressure-Temperature
For T-v diagram, pressure held constant Above the critical point temperature, no mixture region exists Temperature-Specific Volume
Triple Line/Point • Area where all three phases can exist; • Line on P-v and T-v diagrams • Point on P-T diagrams
Two ways a substance can go from solid to vapor: Melts to liquid, then vaporizes to vapor Evaporates directly with out first melting, sublimation Happens at pressures below triple point value Sublimation
Enthalpy-Combination Property • Enthalpy, h, defined as h =u + Pv (kJ/kg) • Also H = U + PV (kJ)
Property Tables • For most substances, relationships among thermodynamic properties too complex to be expressed by simple equations • For these substances tables have been developed from experimentation • Tables have been developed for each region of interest such as superheated vapor and saturated mixture • Separate sets of tables for SI and USCS systems
Temperature = 90°F Pressure = 70.183 kPa Specific Volume Sat liquid = 0.001036 m3/kg Sat vapor = 2.3593 m3/kg Internal Energy Sat liquid = 376.97 kJ/kg Sat vapor = 2494.0 kJ/kg Saturated Tables
Saturated Tables • Subscript f, properties of saturated liquid • Subscript g, properties of a saturated vapor • Subscript fg, difference between the saturated liquid and saturated vapor properties of the same property • ufg = ug - uf
Saturated Liquid-Vapor Mixture • Between saturated liquid line and saturated vapor line is the saturated liquid-vapor mixture region • Temperature-pressure relationship (not independent) • Property of quality x = mvapor/ mtotal • Sat liquid x = 0 • Sat vapor x = 1 • Only valid for saturated liquid-vapor mixture
Single phase region, vapor Compared to sat vapor: Lower pressure (P<Psat at given T) Higher temperature (T>Tsat at given P) Higher v, u, h at a given T or P Superheated Vapor
A compressed liquid may be approximated as a saturated liquid at the given temperature Compressed Liquid
A compressed liquid has: Higher pressure (P>Psat at a given T) Lower temperature (T<Tsat at a given P) Lower specific volume (v < vf at a given P or T) Lower internal energy (u < ufat a given P or T) Lower enthalpy (h < hf at a given P or T) But are not much different, see table 7 Compressed Liquid
Reference State • Tables based on changes in properties, not absolute values • Reference states assigned • Water: Saturated liquid at 0.01°C • R-134a: Saturated liquid at -40°C
Ideal-Gas Equation of State • An alternative to tables is equations of state • Equations of state relate pressure, temperature, specific volume • Equations are specific to substance and range from simple to complex • Simplest is Ideal-Gas equation of state
Ideal-Gas Equation of State • Ideal-gas equation of state Pv=RT where R is called the gas constant P is the absolute pressure T is the absolute temperature v is the specific volume
R is different for each gas R = Ru /M (kJ/kgK) where Ru is the universal gas constant and M the molar mass Ru= 8.31447 kJ/kmolK Ideal-Gas Equation of State
Ideal-Gas Equation of State • Most used as
Characteristics: Low densities High temperatures Low pressures In general above the critical point Ideal Gas
Compressibility Factor • Measure of deviation from ideal-gas behavior • Define a compressibility factor Z for gases • Equation of state becomes Pv=ZRT where Z = 1 for ideal gases
Compressibility Factor • To plot information for different gases need to define normalized pressure and temperature • PR = P/Pcr • TR = T/Tcr • where PR is the reduced pressure and TR is the reduced temperature • And Pcr is the critical pressure and Tcr is the critical temperature
For Gases in General • At low pressure (PR<<1) gases behave as ideal gas regardless of temperature • At high temperatures (TR>2) ideal-gas behavior can be assumes (unless PR>>1) • The deviation of a gas from ideal-gas behavior is greatest near the critical point
Compressibility Factor • Pseudo-reduced specific volume vR = vactual/(RTcr/Pcr)
Energy Analysis of Closed Systems Moving boundary work
Deal with the expansion/ compression of gas in piston-cylinder device Analyze moving boundary work as quasi-equilibrium process Moving Boundary Work
δWb = F ds = PA ds = P dV where P is absolute pressure (always positive) and dV, change in volume, may be positive or negative Moving Boundary Work
Moving Boundary Work • The total boundary work is • Or area under curve on P-V diagram
Moving Boundary Work • To find work need the path function P as a function of V • Look for relationship to be defined in situation.
Example 4-3 What is the relationship between P and V? Moving Boundary Work
Polytropic Process • Polytropic process are one that P and V are related by PVn = C where C and n are constants • Integration results in: • Wb =mR(T2-T1)/(1-n) for n≠1 • W =PV ln(V2/V1)
Energy Balance • For any system Ein– Eout = ΔEsystem • Can be written in rate form, per unit mass form • Also δEin– δEout = dEsystem
For a closed system undergoing a cycle where the initial and final states are the same Ein– Eout = ΔEsystem = 0 Energy Balance for Closed System
Energy Balance for Closed System • In general case: Qnet,in – Wnet,out = ΔEsystem
Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree Two types dependent on process Constant volume, cv Constant pressure, cp Specific Heats
Given Pv=RT, u = u(T), and h = u +Pv Then h = u + RT and h = h(T) Internal Energy, Enthalpy, Specific Heats of Ideal Gases
