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Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa [email protected]

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Page 1: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Gestão de Energia: 2013/2014

Introduction&

Review of ThermodynamicsClass # 1

Prof. Tânia [email protected]

Page 2: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Docentes

• Tânia Sousa– [email protected]

• Carla Silva– [email protected]

• Carlos Silva– [email protected]

• André Pina– [email protected]

Page 3: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Avaliação

• Exame (50%) com nota mínima 9.5 val.• Avaliação Contínua (50%)

– Trabalhos feitos por grupos de 2/3 alunos

– Os trabalhos começam nas aulas e são para terminar em casa

– A avaliação é feita nas aulas e com os trabalhos

• Trazer um portátil por grupo para as aulas práticas

Page 4: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Objectivo

1. Compreender e modelar os fluxos energéticos à escala do país, em sistemas industriais, em edifícios ou equipamentos complexos.

2. Definir acções que permitam racionalizar o uso da energia, quantificando os benefícios económicos e ambientais destas acções.

Page 5: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Gestão de Energia: ConteúdoSemana Teóricas Práticas

21-02-2014 Apresentação. Revisões Termodinâmica

28-02-2014 Balanço Energético Português Exercícios

07-03-2014 Energia Primária Final e e Útil. Diagramas de Sankey Transições Energéticas. Análise da Eficiência de Sistemas Energéticos

Trabalho I (B.E.N)

14-03-2014 Modelos analíticos para a análise energética de sistemas: diagramas de blocos

Trabalho II (Sankey)

21-03-2014Eficiência Energética na Indústria. Regulamento da eficiência energética na indústria (SGCIE).

Exercícios

28-03-2014Eficiência Energética nos edifícios.Regulamentos de eficiência energética nos edifícios.

Trabalho III

04-04-2014 Modelos Input-Output Exercícios

11-04-2014Energia e EconomiaMétodos de contabilização da electricidade primária.

Trabalho IV (Input-Output)

18-04-2014 FÉRIAS FÉRIAS

25-04-2014 FERIADO FERIADO

02-05-2014 Análise Ciclo de Vida Exercícios

09-05-2014 Eficiência energética nos Transportes. Regulamento da eficiência energética nos Transportes

Exercícios

14-05-2014 Auditorias Energéticas Trabalho V (Tranportes)

23-05-2014 Modelação Oferta e Procura de Energia Visita a um Laboratório Tagus Park

30-05-2014 Revisões. Exercícios

4ª feira à tarde 4ª feira manhã e à tarde

Page 6: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents Thermodynamics

• Energy and Entropy Balances for Closed & Open Systems

• Thermodynamic Cycles: power cycle, heat pump & refrigerator cycle

• 1st Pratical Class (exercises)

• Bibliography– “Fundamental of Engineering Thermodynamics”

Shapiro & Moran

Page 7: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T2

• The Portuguese Energetic Balance:– Supply, Conversion & Demand

– Energy CarriersBALANÇO ENERGÉTICO

tep   Total de Carvão Total de PetróleoGás Natural

(*)

Gases o Outros

Derivados

Total de Eectricidade

CalorResíduos

IndustriaisRenováveisSem Hídrica

TOTAL GERAL

2008   4 = 1 a 3 22= 15 + 21 23 30 = 24 a 29 36 = 31 a 35 37 38 46 = 39 a 4547=4+22+23+30+36+37

+38+46

IMPORTAÇÕES 1. 2 327 219 16 608 384 4 163 167   923 984       24 022 754

PRODUÇÃO DOMÉSTICA 2.         1 142 338   39 800 3 190 679 4 372 817

VARIAÇÃO DE "STOCKS" 3. - 223 603 315 673 5 960         - 837 97 193

SAÍDAS 4. 24 949 3 680 661     112 918     17 634 3 836 162 CONSUMO DE ENERGIA PRIMÁRIA

5. 2 525 873 12 612 050 4 157 207   1 953 404   39 800 3 173 882 24 462 216

PARA NOVAS FORMAS DE ENERGIA

6. 2 444 703 1 079 137 2 597 143   -2 810 996 -1 472 450 1 120 1 367 391 3 206 048

CONSUMO DO SECTOR ENERGÉTICO

7.   475 376 56 103   605 301 270 736   3 1 407 519

CONSUMO COMO MATÉRIA PRIMA     1 275 842             1 275 842

DISPONÍVEL PARA CONSUMO FINAL

8. 81 170 9 781 695 1 503 961   4 159 099 1 201 714 38 680 1 806 488 18 572 807

ACERTOS 9. 9 851 - 47 340 - 1 382   12     279 - 38 580

CONSUMO FINAL 10. 71 319 9 829 035 1 505 343   4 159 087 1 201 714 38 680 1 806 209 18 611 387

AGRICULTURA E PESCAS 10.1   358 801 3 359   87 218 2 366   21 451 765

INDÚSTRIAS EXTRACTIVAS 10.2   66 103 8 444   49 882 30 844   4 155 277 INDÚSTRIAS TRANSFORMADORAS

10.3 71 319 1 085 788 1 027 157   1 340 009 1 154 293 38 680 615 382 5 332 628

CONSTRUÇÃO E OBRAS PÚBLICAS

10.4   576 210 5 063   50 490     21 631 784

TRANSPORTES 10.5   6 680 176 6 659   46 677     3 452 6 736 964

SECTOR DOMÉSTICO 10.6   552 680 300 190   1 157 672     1 180 750 3 191 292

SERVIÇOS 10.7   509 277 154 471   1 427 139 14 211   6 579 2 111 677

Page 8: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T2

• 2nd Pratical Class & 1st assignment – Each group analyses the PEB for a specific year and

compares it with 2012 (bring the computer)

• Learning Outcomes:– Be able to retrieve information from the Energetic

Balance of a country/region

– Compute electricity production efficiencies and other 1st law efficiencies for the country level

• Bibliography: – Chap. 2 “Balanço Energético Nacional -

Metodologia de Elaboração, Evolução da Estrutura e do Consumo Energético Primário”, Ramos, A.

– Chap. 2 “Energy Economics”, Bhattacharyya.

Page 9: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• From Primary Energy to Energy Services at different scales

Course Contents - T3

IAASA - Global Energy Assessment 2012

Page 10: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents - T3

Grubler, A. “Energy Transitions”

Energy Transition Energy Transition biomass to coal coal to oil

• World and national patterns of energy use• Energy Transitions

Page 11: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents - T3

• Sankey diagrams for different scales

• 1st and 2nd Law Efficiencies

Page 12: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T3• 2nd Pratical Class & 1st assignment

– Each group draws the Sankey diagram using e-Sankey for the PEB for a specific year for Portugal

• Learning outcomes:– Understand concepts of primary, final & useful energy

– Historical perspective on world energy use & transitions

– Use Sankey diagrams to analyse energy systems

– Understand 1st and 2nd law efficiencies

• Bibliography: – Cap. 2 da sebenta “Gestão de Energia”, Águas, M.

– Chapter 1 & 16 GEA, IAASA

– Cullen and Alwood “The efficient use of energy: Tracing the global flow of energy”, Energy Policy 2010.

Page 13: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Block Diagrams Energy Analysis

• 3th Practical Class– Exercises

• Learning Outcomes– Compute the energy intensity of a product or service,

i.e., the total energy required to produce it

– Compute the impact of efficiency measures on the specific energy consumption

• Bibliography: – Cap. 5 da sebenta “Gestão de Energia”, Águas, M.

Course Contents – T4

Page 14: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Energy use in industry

• SGCIE: Energy efficiency in industry

• 4th Practical Class & 3rd assignment – Each group chooses a case study (e.g. the Secil),

finds the correct data and describes the production process and computes the specific consumption

Course Contents – T5

Page 15: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Learning Outcomes– Apply & understand the SGCIE legislation

• Bibliography: – DL n.º 71/2008; Despachos nº 17449/2008 &

17313/2008

– Chap. 6 “Energy Efficiency and the Demand for Energy Services” Danny Harvey

Course Contents – T5

Page 16: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T6

• Energy use in Buildings– Factors controlling energy use in buildings

– Techniques to reduce energy use:

Page 17: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T6

• RCCTE & RSECE: Energy efficiency in buildings• 5th Practical Class

– Exercises

• Learning Outcomes– Learn about strategies to reduce energy use in buildings

and their impact

– Apply & understand the RCCTE & RSECE

• Bibliography:– Chap. 4 “Energy Efficiency and the Demand for Energy

Services” Danny Harvey

– Decreto-lei n.º 118/2013

Page 18: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents - T7

• IO Analysis at the Macroeconomic scale• Computation of Direct and Indirect Effects of

changes in Demand• 6th Pratical Class & 4th assignment

– Each group computes energy demand scenarios for a country for 2 & 5 & 10 years based on changes in the economic structure & compares with reality

• Application of this methodology to Block Diagrams Analysis

• Bibliography: – Chap. 5 “Ecological Economics”, Common & Stagl.

Page 19: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T8

• Methods to compute primary energy for renewable electricity

• EROI

Page 20: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T8

• Learning Outcomes– Critically evaluate statistics and political goals on

the weight of renewables on primary energy mixes at the country level.

– Understand & apply the concept of EROI

• BibliographyChapter. 14 & 15 from “Energy and the Wealth of Nations”,Hall, C. & Klitgaard, K..

• 7th Practical Class– Exercises

Page 21: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T8

• Energy & Economic Growth & Environment

Page 22: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T8

• Learning Outcomes– Identify the interactions between energy use,

economic growth and environmental quality

• Bibliography:– Chap. 2 & 6 “Energy at the Crossroads” Smil, V.

Page 23: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T9

• Life Cycle Assessment

• 8th Practical Class– Exercises

• Bibliography:

CO2

Bioethanol

DDG

Bioethanol Life Cycle

Page 24: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Energy use in Transports

Course Contents – T10

Page 25: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T10

• Legislation• 9th Practical Class

– Exercises

• Learning Outcomes– Learn about factors that influence energy use in

transports and strategies & technologies that reduce the energy use in and their environmental impact

– Apply & understand the legislation on transports

• Bibliography:– Chap. 5 “Energy Efficiency and the Demand for

Energy Services” Danny Harvey

Page 26: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T11

• Energy Audits– Measurements

– Mass and Energy Balances

– Equipments

• 10th Practical Class– Visita de Estudo (no Tagus Park)

Page 27: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Course Contents – T12

• Tools to Model the Supply and Demand of Energy

• 11th Practical Class– Exercises

• Learning Outcomes– Learn about the energy modeling softwares & their

usefulness

Page 28: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Energy Balance in Closed Systems

Energy Change = Heat + Work

Energy change in the system Flows at the boundaries

p cd U E EdEQ W

dt dt

• 1st Law: Energy Conservation

• U, Ec and Ep

• Energy transfer by Heat

• Energy transfer by Work

• Sign of heat and work fluxes

• Steady state vs. Transient

work

heat

Page 29: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Choosing the boundaries – Flows, Thermodynamic System, Steady vs.

Transient state – flows at the boundaries?

Energy Balance in Closed Systems

Page 30: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Choosing the boundaries – Flows, Thermodynamic System, Steady vs.

Transient state

Energy Balance in Closed Systems

Page 31: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercise:

Energy Balance in Closed Systems

Page 32: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Thermodynamic Cycles

Energy Balance in Closed Systems

• 1st Law efficiencies– Power Cycle

– Heat Pump

– Refrigerator

Power Cycle Refrigerator &Heat Pump Cycles

cycle

in

W

Q

out

cycle

Q

W

in

cycle

Q

W

Page 33: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercise (Homework)

– If P is constant then

– If PV is constant then

Energy Balance in Closed Systems

. .W Fdx P Adx P dV f iW P V V

ln fi i

i

VW PV

V

Page 34: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercise (Homework)

• Exercise:

– Why is it possible that ?

– How much does the electricity of your fridge costs in a month?

Energy Balance in Closed Systems

1

Page 35: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Energy Balance in Open Systems

Energy Change = Heat + Work + Energy in Mass Flow

Enthalpy of component j

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Flows at the boundaries

Mass Change = Mass Flows

, ,in i out ji j

dmm m

dt

i i i ih u p v

Page 36: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercises– 1º Write the energy balance eq.

– 2º Identify energy flows

– 3º Simplify the eq.

– For incompressible liquids at constant pressure:

Energy Balance in Open Systems

water at 50ºC 4.182 kJ/kg.K

h c T

c

Page 37: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Turbines: – Produce work as a result of gas or liquid passing

through a set of blades attached to a shaft free to rotate

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Hydraulic Turbine Wind Turbine

Wmec from Ekin of the wind

Electricity from Epot of the water Electricity from Ekin of the wind

Wind Mill

Page 38: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Turbines: – Produce work as a result of gas or liquid passing

through a set of blades attached to a shaft free to rotate

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Hydraulic Turbine Wind Turbine

Wmec from Ekin of the wind

Electricity from Epot of the water Electricity from Ekin of the wind

Wind Mill

Page 39: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercises– Write the energy

balance eq.

– Identify energy flows

– Simplify the eq.

• What is the energy conversion taking place?

Energy Balance in Open Systems

Castelo de Bode dam

•3 turbines

• medium water fall 80 m

•Installed power: 159 MW

•Medium annual electricity production: 390 GWh

Page 40: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercises– Write the energy

balance eq.

– Identify energy flows

– Simplify the eq.

• Potential energy is converted into electricity and kinetical energy

Energy Balance in Open Systems

Castelo de Bode dam

•3 turbines

• medium water fall 80 m

•Installed power: 159 MW

•Medium annual electricity production: 390 GWh

Page 41: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Compressors (gas) & Pumps (liquids): – Used in aircraft engines, water pumping, natural gas

transport, etc

– Increase the pressure of a gas (compressor) or move fluids or slurries (pumps) using work

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Reciprocating Compressor

Treadle Pump

Pump water using work

Pumps

Pump water using human work

Increase in pressure of gas obtainned from decreasing volume (obtainned with work)

Page 42: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Compressors (gas) & Pumps (liquids): – Used in aircraft engines, water pumping, natural gas

transport, etc

– Increase the pressure of a gas (compressor) or move fluids or slurries (pumps) using work

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Reciprocating Compressor

Treadle Pump

Pump water using work

Pumps

Pump water using human work

Increase in pressure of gas obtainned from decreasing volume (obtainned with work)

Page 43: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercises– 1º Write the energy balance eq.

– 2º Identify energy flows

– 3º Simplify the eq.

– Ideal gas model:

– The need to cool after compression

Energy Balance in Open Systems

4

( )

CH 2.226 kJ/kg.K

PV NRT

u u T

h c T

c

Underground storing of natural gas in Carriço

Storing Pressure: 180 bar

Storing capacity: 2 155 GWh

Page 44: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Heat Exchangers: – Used in power plants, air conditioners, fridges,

liquefication of natural gas, etc

– Transfer energy between fluids at different temperatures

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Direct Contact Heat Exchanger

Counter-flow Heat exchanger

Direct Flow Heat Exchanger

Page 45: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Heat Exchangers: – Used in power plants, air conditioners, fridges,

liquefication of natural gas, etc

– Transfer energy between fluids at different temperatures

Energy Balance in Open Systems

22

, ,2 2ji

in i i i out j j ji j

vvdEQ W m h gz m h gz

dt

Direct Contact Heat Exchanger

Counter-flow Heat exchanger

Direct Flow Heat Exchanger

Page 46: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Exercises (homework)– 1º Write the energy balance eq.

– 2º Identify energy flows

– 3º Simplify the eq.

• Discuss boundaries

Energy Balance in Open Systems

Liquefaction of natural gas

T=-162ºC

Decrease in volume: 1/600

Page 47: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• Coal power plant:

Power cycle revisited

Power Cycle Refrigerator

Page 48: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

The state variable: Entropy

• Entropy is the state variable that gives unidirectionality to time in physical processes ocurring in isolated & adiabatic systems.– Hot coffee in a cold room gets colder and not

hotter

– Radiating energy is received by the Earth from the sun and by outer space from the earth and not the other way around.

– If the valve of the tyre is opened, air gets out and not in

Page 49: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

Entropy Balance in Closed Systems

Entropy Change = Entropy transfer in the form of heat + entropy production

Entropy change in the system

Flows at the boundariesdS Q

dt T

• Meaning of

• 2st Law:

• >0

• In adiabatic systems…

• Entropy transfer by Heat & sign

• Steady state vs. Transient

work

heat

It is not a flow at the boundary

Not relevant for entropy balance

Page 50: Gestão de Energia: 2013/2014 Introduction & Review of Thermodynamics Class # 1 Prof. Tânia Sousa taniasousa@ist.utl.pt

• 2nd Law: In an adiabatic system the entropy must not decrease

• Suppose the system is adiabatic and that T2>T1

• 2nd Law: the arrow of time

Entropy Balance in Closed Systems

1 2

1 2

0

0

dS

dt

dS dSdS Q Q

dt dt dt T T

T2 T1

1 2

1 2

0

0 0

dS

dt

dS dSdS Q Q

dt dt dt T T

T2 T1