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MAE 219: THERMODYNAMICS
by
Professor YVES NGABONZIZA
MAE 219: THERMODYNAMICS I
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Syllabus Overview
Capstone course
Communication Platform (Blackboard, E-Portfolio)
E-Portfolio
Studio Hour
Term paper (Report Format)
Lab ExperimentMAE 219: THERMODYNAMICS I
1. CONCEPTS AND DEFINITIONS
Closed system (control mass) consist of a fixed amount of mass, and no mass can cross its boundary
Open system (control volume) involves mass flow
Properties: Intensive: independent of the mass of the s/m
e.g. : T, pressure, density
Extensive: depend on system size
e.g.: mass, volume
MAE 219: THERMODYNAMICS I
Conservation of energy:
potential energy + kinetic energy = constant
(P.E.) (K.E.)
Thermal equilibrium:
Two bodies are in thermal equilibrium if they have the same temperature
Otherwise, temperature moves from hot medium to cold medium
MAE 219: THERMODYNAMICS I
Zeroth Law of Thermodynamics:
If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other
Source: http://www.grc.nasa.gov/WWW/K-12/airplane/Images/thermo0.gif
MAE 219: THERMODYNAMICS I
Units
SI US
Mass kg slug
Force N lb
Distance m ft
Velocity m/s ft/s
Acceleration m/s2 ft/s2
Density kg/m3 lb/ft3
Temperature K 0 F
MAE 219: THERMODYNAMICS I
Temperature Units Conversion
T(K)=T(oC) + 273
T(R)=T(oF) + 460
T(R)=1.8T(K)
T(oF)=1.8T(oC) + 32
MAE 219: THERMODYNAMICS I
Pressure:
Normal force exerted by a fluid per unit area
Unit: Pa (SI) or psi (US)
Pgage = Pabs – Patm
Pabs=actual (absolute) pressure
Note: pressure measuring devices read 0 pressure in atmosphere
MAE 219: THERMODYNAMICS I
p = f(z)
2
112)( dzgPPP
gdzdp
+z
pA=pB=pC=Patm+ ghPatm
AB
C
h
MAE 219: THERMODYNAMICS I
Example
The pressure in a pressurized water tank is measured by a multi-fluid manometer. The gage pressure of air in the tank is to be determined.
The densities of mercury, water, and oil are given to be 13,600, 1000, and 850 kg/m3, respectively. Consider h1=0.2m, h2=0.3m and h3=0.46
H.W. 1
MAE 219: THERMODYNAMICS I
2. PROPERTIES OF A PURE SUBSTANCE
2.1. Pure SubstanceA pure substance has a homogeneous and invariable chemical composition and may exist in more than one phase.
2.2. Phases of a pure substance
Solid Phase: molecules are at relatively fixed positionLiquid phase: groups of molecules move about each otherGas phase: molecules are far apart from each other. Molecules move
randomly
MAE 219: THERMODYNAMICS I
2.3. Phase change processes
Let's consider the results of heating liquid water from 20C, 1 atm while keeping the pressure constant.
As liquid water is heated while the pressure is held constant, the following events occur.
Process 1-2:
The temperature and specific volume will increase from the compressed liquid, or subcooled liquid, state 1, to the saturated liquid state 2. In the compressed liquid region, the properties of the liquid are approximately equal to the properties of the saturated liquid state at the temperature.
MAE 219: THERMODYNAMICS I
Process 2-3:
At state 2 the liquid has reached the temperature at which it begins to boil (100C ), called the saturation temperature, and is said to exist as a saturated liquid. Properties at the saturated liquid state are noted by the subscript f and v2 = vf. At state 3 the liquid and vapor phase are in equilibrium and any point on the line between states 2 and 3 has the same temperature and pressure.
MAE 219: THERMODYNAMICS I
Process 3-4:
At state 4 a saturated vapor exists and vaporization is complete. The subscript g will always denote a saturated vapor state. Note v4 = vg.
MAE 219: THERMODYNAMICS I
Process 4-5:
If the constant pressure heating is continued, the temperature will begin to increase above the saturation temperature, 100 C in this example, and the volume also increases. State 5 is called a superheated state because T5 is greater than the saturation temperature for the pressure and the vapor is not about to condense.
MAE 219: THERMODYNAMICS I
This constant pressure heating process is illustrated in the following figure.
Figure : T-ν diagram for the heating of water at constant pressure
MAE 219: THERMODYNAMICS I
Thermodynamic properties at the saturated liquid state and saturated vapor state are given in Table A-4 as the saturated temperature table and Table A-5 as the saturated pressure table. These tables contain the same information.
The saturation pressure is the pressure at which phase change will occur for a given temperature. In the saturation region the temperature and pressure are dependent properties; if one is known, then the other is automatically known.
Thermodynamic properties for water in the superheated region are found in the superheated steam tables, Table A-6.
MAE 219: THERMODYNAMICS I
2.4. Property diagrams for phase-change processes
In this section, we will discuss the T-V, P-V and P-T diagrams for pure substances
T-V diagram
MAE 219: THERMODYNAMICS I
P-V Diagram
The P-V diagram of a pure substance is very much like the T-V diagram, but the T=constant line on this diagram have a downward trend.
MAE 219: THERMODYNAMICS I
P-T Diagram
This diagram is often called the phase diagram since all phases are separated.
The triple point of water is 0.01oC (= 273 K), 0.6117 kPa (See Table 3-3).
The critical point of water is 373.95oC, 22.064 MPa (See Table A-1).
MAE 219: THERMODYNAMICS I
Saturated liquid-vapor mixture
The analysis of the mixture is based on the proportion of the liquid and vapor phases in the mixture.
Quality x is defined as
xmass
mass
m
m msaturated vapor
total
g
f g
The quality is zero for the saturated liquid and one for the saturated vapor (0 ≤ x ≤ 1).
MAE 219: THERMODYNAMICS I
We note V V V
m m m
V mv V m v V m v
f g
f g
f f f g g g
, ,
mv m v m v
vm v
m
m v
m
f f g g
f f g g
Recall the definition of quality x
xm
m
m
m mg g
f g
Then
m
m
m m
mxf g
1
Note, quantity 1- x is often given the name moisture. The specific volume of the saturated mixture becomes
v x v xvf g ( )1
MAE 219: THERMODYNAMICS I
The form that we use most often is
v v x v vf g f ( )
It is noted that the value of any extensive property per unit mass in the saturation region is calculated from an equation having a form similar to that of the above equation. Let Y be any extensive property and let y be the corresponding intensive property, Y/m, then
yY
my x y y
y x y
where y y y
f g f
f fg
fg g f
( )
The term yfg is the difference between the saturated vapor and the saturated liquid values of the property y; y may be replaced by any of the variables v, u, h, or s.
MAE 219: THERMODYNAMICS I
The enthalpy is a convenient grouping of the internal energy, pressure, and volume and is given by
H U PV
The enthalpy per unit mass ish u Pv
How to Choose the Right Table
The correct table to use to find the thermodynamic properties of a real substance can always be determined by comparing the known state properties to the properties in the saturation region. Given the temperature or pressure and one other property from the group v, u, h, and s, the following procedure is used. For example if the pressure and specific volume are specified, three questions are asked: For the given pressure,
MAE 219: THERMODYNAMICS I
Is ?
Is ?
Is ?
v v
v v v
v v
f
f g
g
The answer to one of these questions must be yes. If the answer to the first question is yes, the state is in the compressed liquid region, and the compressed liquid tables are used to find the properties of the state. If the answer to the second question is yes, the state is in the saturation region, and either the saturation temperature table or the saturation pressure table is used to find the properties. Then the quality is calculated and is used to calculate the other properties, u, h, and s. If the answer to the third question is yes, the state is in the superheated region and the superheated tables are used to find the other properties.
Some tables may not always give the internal energy. When it is not listed, the internal energy is calculated from the definition of the enthalpy as
u h Pv
MAE 219: THERMODYNAMICS I
Examples
1. A rigid tank contains 50 kg of saturated liquid water at 90oC. Determine the pressure in the tank and the volume of the tank.
2. A piston-cylinder device contains 2 ft3 of saturated water vapor at 50 psi pressure. Determine the temperature and the mass of the vapor inside the cylinder.
MAE 219: THERMODYNAMICS I
Solution:
1. Using Table A-4, at 90oC, P=70.183 kPa and ν=0.001036 m3/kg
Then, the volume V = ν *m = 0.0518m3
2. Using Table A5-E, at P=50psi, T=280.99oF
νg=8.5175 ft3/lbm
The mass lbmlbmft
ftVm 235.0
/5175.82
3
3
MAE 219: THERMODYNAMICS I
2.5. Equations of State
The relationship among the state variables, temperature, pressure, and specific volume is called the equation of state. We now consider the equation of state for the vapor or gaseous phase of simple compressible substances.
Ideal Gas
Based on our experience in chemistry and physics we recall that the combination of Boyle’s and Charles’ laws for gases at low pressure result in the equation of state for the ideal gas as
where R is the constant of proportionality and is called the gas constant and takes on a different value for each gas. If a gas obeys this relation, it is called an ideal gas. We often write this equation as
Pv RTMAE 219: THERMODYNAMICS I
The gas constant for ideal gases is related to the universal gas constant valid for all substances through the molar mass (or molecular weight). Let Ru be the universal gas constant. Then,
RR
Mu
And we know mVV
m
The ideal gas equation of state becomes mRTpV
For fixed mass at 2 different phases
2
2
1
1
TpV
TpV
MAE 219: THERMODYNAMICS I
Example:
Determine the mass of the air in a room whose dimensions are 4m*5m*6m at 100 kPa and 25oC
Solution:
Using Table A-1, R of the air is 0.287 kPa.m3/kg.K
25oC = (25+273)K =298K
V = (4*5*6) m3 = 120m3
kgkgRTpV
m 3.140298*287.0
120*100
MAE 219: THERMODYNAMICS I
The ideal gas equation of state is used when (1) the pressure is small compared to the critical pressure or (2) when the temperature is twice the critical temperature and the pressure is less than 10 times the critical pressure.
2.6. Compressibility Factor
The compressibility factor Z determines how much the ideal gas equation of state deviates from the actual gas behavior.
RTpV
Z
For an ideal gas Z = 1, and the deviation of Z from unity measures the deviation of the actual P-V-T relation from the ideal gas equation of state.
or
ideal
actualZ
MAE 219: THERMODYNAMICS I
2.7. Other Equations of State
Many attempts have been made to keep the simplicity of the ideal gas equation of state but yet account for the intermolecular forces and volume occupied by the particles.
Three of these are
(a) Van der Waals: ( )( )P
a
vv b R T
2
where
aR T
Pb
RT
Pcr
cr
cr
cr
27
64 8
2 2
and
accounts for intermolecular forces
accounts for volume occupied by the gas molecules
2a
b
MAE 219: THERMODYNAMICS I
(b) Beattie-Bridgeman:
where
The constants a, b, c, Ao, Bo for various substances are found in Table 3-4.
( c ) Benedict-Webb-Rubin:
The constants for various substances appearing in the Benedict-Webb -Rubin equation are given in Table 3-4.
H.W. 2MAE 219: THERMODYNAMICS I