Transcript Slide 1
Chapter 3: Thermodynamic Properties of Pure Substances
A snowflake at high magnification. The solid phase of water in one of its forms. (Courtesy of Kenneth G. Libbrecht, Cal Tech) ThermoNet Thermodynamics: An Integrated Learning System P.S. Schmidt, O.A. Ezekoye, J.R. Howell and D.K. Baker Copyright (c) 2005 by John Wiley & Sons, Inc
3.1 STATE PRINCIPLE Any two independent intensive thermodynamic properties are sufficient to describe the state of a system containing a single pure substance.
Chapter 3: Thermodynamic Properties of Pure Substances
3.2 Intensive and Extensive Properties
• • •
The value of an extensive the mass of the system. property is dependent of The value of an intensive property is independent of the mass of the system. Partition box P o , T o , V o , m o P 1 T 1 V 1 m 1 P 2 T 2 V 2 m 2 P T V 0 0 0 m 0 = P = T 1
V 1 1 m 1 = P 2
= T 2
Intensive Prop Intensive Prop
V 2 m
2 Extensive Prop
Extensive Prop
•
Try specific volume: v = V/m
v 0 = v 1 = v 2
Intensive Property Chapter 3: Thermodynamic Properties of Pure Substances
3.2 Intensive and Extensive Properties Property Mass Temperature Pressure Volume Internal Energy Enthalpy Extensive m V U H Intensive T P v = V/m ( specific volume) u = U/m ( specific internal energy) h = H/m ( specific enthalpy)
•
Any extensive property can be made intensive (specific) by dividing by mass.
Chapter 3: Thermodynamic Properties of Pure Substances
3.3 Pure Substances
• •
Are composed of a single chemical species (e.g., either O 2 or CO 2 but not a mixture of O 2 and CO 2 ).
May exist in more than one phase (e.g., solid and liquid) A mixture of snow, ice, liquid water and water vapor is a pure substance.
Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface
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Constant Pressure Heating in Piston-Cylinder at P = 1 atm Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface
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Constant Pressure Heating in Piston-Cylinder at P = 2 atm Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface
• •
Regions on T-v Diagram Note directions of Isobars Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface PowerPoint frozen? Click here and try again Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface
• •
Regions on P-v Diagram Note directions of Isotherms Chapter 3: Thermodynamic Properties of Pure Substances
3.3.1 Phase Change and P-v-T Surface
•
Three-Dimensional P-v-T Surface Chapter 3: Thermodynamic Properties of Pure Substances
3.4 Liquid-Vapor Tables
• • • •
For Ideal Gases (treated later):
– –
Pv = RT Very simple and accurate relation No similar relation exists for liquids, saturated liquid vapor mixtures or superheated vapors Typically superheated vapors do not obey the ideal gas law.
Use data tabulated based on T and P
– – –
Compressed Liquid Tables Saturated Liquid-Vapor Tables Superheated Vapor Tables Chapter 3: Thermodynamic Properties of Pure Substances
3.5 Saturation and Quality
•
Property Notation (Subscripts):
– – – –
L V = = LV SAT Saturated Liquid Saturated Vapor values (e.g., v LV = v V (e.g., v L (e.g., v V - v L = Saturated Mixture ) (T SAT and u L and u V ) ) = Difference between saturated vapor and liquid and P SAT ) Chapter 3: Thermodynamic Properties of Pure Substances
3.5 Saturation and Quality
•
Quality ( x ): Mass Fraction of Saturated Vapor Chapter 3: Thermodynamic Properties of Pure Substances
3.5 Saturation and Quality
• •
Specific Volume (v) of Saturated Liquid Vapor Mixture with quality x v = v L + xv V Quality of Saturated Liquid Vapor Mixture with Specific Volume (v) x
v V
v L L
L v LV Chapter 3: Thermodynamic Properties of Pure Substances
3.5 Saturation and Quality
•
Determine Phase if:
– – –
P = 100 kPa and v = 0.001000 m 3 /kg P = 100 kPa and T = 100 0 C P = 100 kPa and v = 1.0000 m 3 /kg Chapter 3: Thermodynamic Properties of Pure Substances
3.6 Compressed (Subcooled) Liquids P = 1000 kPa & T = 105 0 C P SAT (105 0 C) = 122.35 kPa Since P > P SAT (T)
Compressed Liquid T = 70 0 F
&
P = 14.7 psia T SAT (14.7 psia) = 212 0 F Since T < T SAT (P)
Subcooled Liquid
•
Subscript CL = Compressed Liquid : e.g., v CL Chapter 3: Thermodynamic Properties of Pure Substances
3.6 Incompressible Liquid Approx (ICL)
• • • •
v CL
(70 0
C, 5000 kPa) = 0.001020 m 3 /kg v L
(70 0
C) = 0.00102 m 3 /kg v L (5000 kPa) = 0.00129 m 3 /kg v CL
(T,P)
v L
(T)
ICL Chapter 3: Thermodynamic Properties of Pure Substances
3.6 Incompressible Liquid Approx (ICL)
• • •
v CL
(T,P)
v L
(T)
u CL
(T,P)
u L
(T)
h CL
(T,P)
–
h L
(T)
+ v Recall h = u + P v
L (T) [P – P SAT (T)] h sensitive to P
–
If P
P SAT
(T)
h L
(T) >>
v L (T) [P – P SAT (T)] h CL
(T,P)
h L
(T)
Chapter 3: Thermodynamic Properties of Pure Substances
3.7 Superheated Vapor T = 400 0 C & P = 3000 kPa T SAT (3000 kPa) = 233.9
Since T > T SAT
(P)
0 C Superheated Vapor Chapter 3: Thermodynamic Properties of Pure Substances
3.7 Superheated Vapor Chapter 3: Thermodynamic Properties of Pure Substances
3.8 Gases
• • • • •
Molecules are relatively far apart Do not feel one another’s presence except during collisions Have a low density Are highly compressible In next two slides, compare
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Liquid-Vapor working fluid in steam engine
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Gas working fluid in gas turbine Chapter 3: Thermodynamic Properties of Pure Substances
3.8 Gases PowerPoint frozen? Click here and try again Chapter 3: Thermodynamic Properties of Pure Substances
3.8 Gases PowerPoint frozen? Click here and try again Chapter 3: Thermodynamic Properties of Pure Substances
3.9 Ideal Gas Law
• •
Universal Gas Constant value.
Particular Gas Constant unique value.
( R ): Each gas has a Chapter 3: Thermodynamic Properties of Pure Substances
3.10 Compressibility Factor
•
Use if not IGL and vapor tables not available
Z P R Pv RT P P CR T R P T CR
Chapter 3: Thermodynamic Properties of Pure Substances
3.11 Other Equations of State
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Van der Waals’ equation
• P v RT b a v 2
Redlich-Kwong Equation
P RT RK a RK RK T 1 / 2 • •
Benedict-Webb-Rubin Equation of State
P RT v
Virial Equation of State
P RT v 0 C T 0 2 ) 1 B v 1 v 2 C v 2 v 3 ......
a v 6 c 1 / v 2 exp v 2
Chapter 3: Thermodynamic Properties of Pure Substances
3.12 Internal Energy and Enthalpy
• • •
Internal Energy
– –
If not an ideal gas, u = u(T,P) If ideal gas , u = u(T)
u(P) Enthalpy
– – –
Recall h = u + Pv For an Ideal Gas , Pv = RT
h = u(T) + RT Therefore for ideal gas , h = h(T)
h(P) T, u and h are dependent properties for ideal gases Chapter 3: Thermodynamic Properties of Pure Substances
3.13 Heat Capacities and Specific Heats
• • •
Approximately,
C Energy T
Heat capacity ( C V ) and specific heat capacity ( c V ) for constant volume
C v U T v and c v
process
u T v
Heat capacity ( C P ) and specific heat capacity ( c P ) for constant pressure
C P H T P and c P
process
h T P
Chapter 3: Thermodynamic Properties of Pure Substances
3.13 Specific Heats for Ideal Gases
•
For an ideal gas , h = h(T)
h(P) and
c P h T P dh dT h T 2 T 1 •
Similarly, for ideal gas u = u(T)
u(V) and
c V u T V du dT u T 2 T 1
Chapter 3: Thermodynamic Properties of Pure Substances
3.13 Specific Heats for Ideal Gases Chapter 3: Thermodynamic Properties of Pure Substances
3.13 Specific Heats for Ideal Gases
• • • • T 2 T 1 T 2 T 1
R = c P – c V For monatomic gases (e.g., He, Ar, Ne)
–
c V = 3R/2 = Constant
–
c P = 5R/2 = Constant
u = c V
T only if c V
h = c P
T only if c P = constant = constant Chapter 3: Thermodynamic Properties of Pure Substances
3.13 Specific Heats for Solids and Liquids
•
For incompressible solids and liquids ,
– –
c P = c V Sometimes denoted as c
h T 2 T 1 cdT
Chapter 3: Thermodynamic Properties of Pure Substances
3.14 Ideal Gas Tables
• • •
Unlike steam tables, pressure not tabulated Use Pv = RT to relate P, v and T Use tables to relate T, u and h Chapter 3: Thermodynamic Properties of Pure Substances
3.15 Some Other Thermodynamic Properties
• • •
Isothermal Compressibility (
k
)
1 v P T
Coefficient of Thermal Expansion (
b
)
1 v v T P dV V b dT k dP
Joule Thompson Coefficient (
m
)
m
T
P
h
Chapter 3: Thermodynamic Properties of Pure Substances