ME 300 Thermodynamics II 1

ME 300 – Thermodynamics II

Prof. S. H. FrankelFall 2006

ME 300 Thermodynamics II 2

Week 1

•Introduction/Motivation•Review•Unsteady analysis – NEW!

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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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Introductions• Instructor: Prof. S. H. Frankel• Office: ME 165/Chaffee 125• Office/cell phone: 765-494-1507/765-404-6067• Email: frankel@ecn.purdue.edu or

frankel.steven@gmail.com• 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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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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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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Key Definitions• Property

• State• Process• Cycle• Equilibrium and Quasi-Equilibrium process

• Dimensions/Units

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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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Key Cycle Relations

• First Law • Second Law

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Inside the “circle”

HEAT ENGINE

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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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Common Systems

• Rigid tank• Piston-cylinder• Steady-flow device

– Nozzle/Diffuser– Compressor/Turbine– Heat Exchanger– Mixing chamber– Throttle

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These devices are real!

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Governing Equations - mass

( ) /cvi e av

dm m m m dA V Adt

ρ υ= − = ⋅ =∑ ∑ ∫ V n

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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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Governing Equations - entropy

jcvi i e e cv

j

QdS m s m sdt T

σ= − + +∑ ∑ ∑

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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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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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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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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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Pure substance with phase change

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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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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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Evaluating Enthalpy Change

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Evaluating Entropy Change

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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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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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Today’s Outline

• Review (continued) - Example• Unsteady flow• Governing equations• Examples

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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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Example 8-77: Solution

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Example 8-77: Solution

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Example 8-77: Solution

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Unsteady Processes

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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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Illustrations

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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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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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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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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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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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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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Example 5-12

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Example 5-12

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Example 5-12

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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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Today’s Outline

• Unsteady flow examples

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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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Example 5-135E

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Example 5-135E

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Example 5-135E

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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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Example 7-212

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Example 7-212

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Example 7-212

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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