me 300 thermodynamics ii fall 2006 - purdue … 300 thermodynamics ii 3 ... ammonia, propane •...
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ME 300 Thermodynamics II 1
ME 300 – Thermodynamics II
Prof. S. H. FrankelFall 2006
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ME 300 Thermodynamics II 2
Week 1
•Introduction/Motivation•Review•Unsteady analysis – NEW!
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ME 300 Thermodynamics II 3
Today’s Outline
• Introductions/motivations• Review
– Definitions– Cycles and systems– First and Second Law– Properties and their evaluation– Problem solving technique
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ME 300 Thermodynamics II 4
Introductions• Instructor: Prof. S. H. Frankel• Office: ME 165/Chaffee 125• Office/cell phone: 765-494-1507/765-404-6067• Email: [email protected] or
[email protected]• Office hours: MWF 11:30-12:30PM in ME 165 or by appt.• Research website: http://ristretto.ecn.purdue.edu• Class website: http://widget.ecn.purdue.edu/~me300• Section website:
http://ristretto.ecn.purdue.edu/class/~me300.html• Textbook: Fundamentals of Engineering
Thermodynamics, Moran and Shapiro, 5th Edition
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ME 300 Thermodynamics II 5
Major topic outline/Deliverables• Motivation• Brief overview of
governing equations• Advanced 2nd law
analysis• Mixtures• HVAC theory and
applications• Combustion• Power cycle analysis
• Reading/HW assignments every class
• Use of EES software for advanced analysis
• Three exams and one final exam
• Syllabus/Course policy
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ME 300 Thermodynamics II 6
Motivation• Why study thermodynamics?
– Important for design and analysis of any device/system that involves interchange between work and heat
– Key applications related to energy and the environment include steam power plants, gas turbine engines, internal combustion engines, refrigeration, and air-conditioning, etc.
• What’s new this time around?– Advanced concepts: unsteady systems, exergy
analysis, new applications to HVAC, combustion, more complex cycle analysis and more . . .
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ME 300 Thermodynamics II 7
Key Definitions• Property
• State• Process• Cycle• Equilibrium and Quasi-Equilibrium process
• Dimensions/Units
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ME 300 Thermodynamics II 8
Main Focus
HIGH TEMP.RESERVOIR, TH
HIGH TEMP.RESERVOIR, TH
HEAT ENGINE
REFRIGE-RATOR/HEAT
PUMP
LOW TEMP.RESERVOIR, TL
LOW TEMP.RESERVOIR, TL
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ME 300 Thermodynamics II 9
Key Cycle Relations
• First Law • Second Law
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ME 300 Thermodynamics II 10
Inside the “circle”
HEAT ENGINE
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ME 300 Thermodynamics II 11
Generic SystemInlet
Open vs. closed
Steady vs. unsteady
Rigid vs. non-rigid
Air etc. vs. phase-changesubstance
Outlet1
3
SystemboundaryInlet
2
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ME 300 Thermodynamics II 12
Common Systems
• Rigid tank• Piston-cylinder• Steady-flow device
– Nozzle/Diffuser– Compressor/Turbine– Heat Exchanger– Mixing chamber– Throttle
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ME 300 Thermodynamics II 13
These devices are real!
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ME 300 Thermodynamics II 14
Governing Equations - mass
( ) /cvi e av
dm m m m dA V Adt
ρ υ= − = ⋅ =∑ ∑ ∫ V n
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ME 300 Thermodynamics II 15
Governing Equations - energy 2 2
( ) ( )2 2
cvi i e e cv cv
dE V Vm h gz m h gz Q Wdt
= + + − + + + −∑ ∑
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ME 300 Thermodynamics II 16
Governing Equations - entropy
jcvi i e e cv
j
QdS m s m sdt T
σ= − + +∑ ∑ ∑
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ME 300 Thermodynamics II 17
Governing Equations - all
2 2
; ( / )
( ) ( )2 2
cvi e
cvi i e e cv cv
jcvi i e e cv
j
dm m m m AVdt
dE V Vm h gz m h gz Q Wdt
QdS m s m sdt T
υ
σ
= − =
= + + − + + + −
= − + +
∑ ∑
∑ ∑
∑ ∑ ∑
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ME 300 Thermodynamics II 18
Special Case: Closed System
( )
sys
sys sys sys
jsys sys
j
m const
E U KE PE Q W
QS
Tσ
=
∆ = ∆ + ∆ + ∆ = −
∆ = +∑
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ME 300 Thermodynamics II 19
Property Evaluation
• Pure substance
• Simple compressible substance
• Key properties• State principle• State relations• Ideal gas vs. pure substance with phase-change
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ME 300 Thermodynamics II 20
Ideal Gas (IG)
• Gases at low pressure and high temperature relative to critical point values– Low density– Neglects volume of molecules– Neglects intermolecular forces– Equation of state
– Internal energy and enthalpy only function of temperature; entropy still function of T and P
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ME 300 Thermodynamics II 21
Pure substance with phase change
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ME 300 Thermodynamics II 22
Property Tables
• Saturated liquid/vapor states (T/P) - quality• Superheated vapor• Compressed (subcooled) liquid• Water, R134a, Ammonia, Propane• Specific heats• Ideal gas properties of air (A-22)• Ideal gas properties of gases (A-23)
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ME 300 Thermodynamics II 23
Tie-in to Governing Equations• Recall conservation of energy (1st law):
• Apply to steady, single-inlet, single-outlet adiabatic rigid control volume neglecting PE changes:
2 2
( ) ( )2 2
cvi i e e cv cv
dE V Vm h gz m h gz Q Wdt
= + + − + + + −∑ ∑
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ME 300 Thermodynamics II 24
Evaluating Enthalpy Change
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ME 300 Thermodynamics II 25
Evaluating Entropy Change
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ME 300 Thermodynamics II 26
Problem Solving Method• List what you are given• List what you are asked to find• Draw and label sketch and identify system
(open/closed?)• List assumptions • Identify and fix your states!• Identify special processes (Is anything constant?)• Develop governing equations• Substitute numerical values identifying data source• Check units!• Examine your answer critically• Comment
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ME 300 Thermodynamics II 27
Summary• Appreciate intimate connection between your
system and the appropriate form of the governing equations
• Appreciate mathematical and physical meaning of terms in governing equations
• Evaluation of properties (changes) differs for ideal gas vs. pure/phase change substance
• Problem solving technique complements thermodynamic knowledge (above)
• Next time . . . Examples and unsteady flow
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ME 300 Thermodynamics II 28
Today’s Outline
• Review (continued) - Example• Unsteady flow• Governing equations• Examples
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ME 300 Thermodynamics II 29
Example 8-77• Liquid water at 200kPa and
20C is heated in a chamber by mixing it with superheated steam at 200kPa and 300C. Liquid water enters the mixing chamber at a rate of 2.5kg/s and the chamber is estimated to lose heat to the surroundings at a rate of 600kJ/min. If the mixture leaves the chamber at 200kPa and 60C, determine (a) mass flow rate of superheated steam and (b) rate of entropy production.
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ME 300 Thermodynamics II 30
Example 8-77: Solution
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ME 300 Thermodynamics II 31
Example 8-77: Solution
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ME 300 Thermodynamics II 32
Example 8-77: Solution
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ME 300 Thermodynamics II 33
Unsteady Processes
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ME 300 Thermodynamics II 34
Motivation• Unsteady flow processes involve changes within the
CV with time• Examples include (see next slide):
– Charging a rigid vessel from supply line– Discharging fluid from pressurized vessel– Driving a gas turbine with pressurized air stored in a large
container– Start-up or shutdown of engines, devices, etc.
• Unsteady processes start and end over some finite time period vs. rate
• Unsteady flow systems, while usually fixed in space, may involve moving boundaries and hence boundary work
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ME 300 Thermodynamics II 35
Illustrations
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ME 300 Thermodynamics II 36
Uniform Flow/Uniform State Assumption
• Most unsteady flow processes invoke the uniform-flow assumption:– Fluid flow at inlet/exit is
uniform and steady– Fluid properties do not
change with time or position over cross-section e.g. single value suffices
• Uniform state assumes intensive properties within CV are uniform with position at each instant e.g. slow process
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ME 300 Thermodynamics II 37
Governing Equations - Mass
cvi e
dm m mdt
= −∑ ∑Integrate term by term wrt time from initial state 1 to final state 2 . . .
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ME 300 Thermodynamics II 38
Governing Equations - Energy
2 2
( ) ( )2 2
cvi i e e cv cv
dE V Vm h gz m h gz Q Wdt
= + + − + + + −∑ ∑Integrate term by term wrt time from initial state 1 to final state 2 . . .
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ME 300 Thermodynamics II 39
Governing Equations - Entropy
jcvi i e e cv
j
QdS m s m sdt T
σ= − + +∑ ∑ ∑Integrate term by term wrt time from initial state 1 to final state 2 . . .
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ME 300 Thermodynamics II 40
Typical simplifications• Charging a tank e.g.
tank filling– Initially evacuated tank– Initial mass is zero– No mass exiting
• Discharging a tank e.g. tank empyting– Initial mass/state
known– No mass entering
2
2 2
2 2
i
i i
ji i cv
j
m mm e m h Q W
Qm s m s
Tσ
=
= + −
= + +∑
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ME 300 Thermodynamics II 41
Example 5-12• A rigid, insulated tank that
is initially evacuated is connected through a valve to a supply line that carries steam at 1MPa and 300C. Now the valve is opened, and steam is allowed to flow slowly into the tank until the pressure reaches 1MPa, at which point the valve is closed. Determine the final temperature of the steam in the tank.
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ME 300 Thermodynamics II 42
Example 5-12
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ME 300 Thermodynamics II 43
Example 5-12
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ME 300 Thermodynamics II 44
Example 5-12
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ME 300 Thermodynamics II 45
Summary
• Governing equations for unsteady flow processes derived by integrating general equations wrt time
• Uniform state/flow assumption often employed• Besides inlet and exit states, unsteady flow
processes require specification or determination of initial and final states
• Without mass flow, equations reduce to those for closed system, as expected
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ME 300 Thermodynamics II 46
Today’s Outline
• Unsteady flow examples
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ME 300 Thermodynamics II 47
Example 5-135E• A 4-ft3 rigid tank contains
saturated refrigerant-134a at 100psia. Initially, 20% of volume is occupied by liquid and rest by vapor. A valve at the top of the tank is now opened, and vapor is allowed to escape slowly from the tank. Heat is transferred to the refrigerant such that the pressure inside the tank remains constant. The valve is closed when the last drop of liquid in the tank is vaporized. Determine the total heat transfer for this process.
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ME 300 Thermodynamics II 48
Example 5-135E
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ME 300 Thermodynamics II 49
Example 5-135E
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ME 300 Thermodynamics II 50
Example 5-135E
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ME 300 Thermodynamics II 51
Example 7-212• A 0.25m3 insulated piston-
cylinder device initially contains 0.7kg of air at 20C. At this state, the piston is free to move. Now air at 500kPa and 70C is allowed to enter the cylinder from a supply line until the volume increases by 50%. Using constant specific heats at room temperature, determine (a) final temperature, (b) amount of mass that entered, (c) work done, and (d) entropy generation.
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ME 300 Thermodynamics II 52
Example 7-212
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ME 300 Thermodynamics II 53
Example 7-212
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ME 300 Thermodynamics II 54
Example 7-212
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ME 300 Thermodynamics II 55
Summary
• Unsteady flow problems involve a start (“now”) and an end (“until”)
• Distinguish between charging (filling) and discharging (empyting)
• Use proper form of governing equations• Invoke uniform state/uniform flow assumption• Know your working fluid so you evaluate
properties correctly e.g. IG vs. pure substance