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L9 Thermo - Thermodynamics Agenda $ Dissipation $ Thermal...

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1 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold Thermodynamics ! Senturia, Ch. 11 " # Agenda $ Dissipation $ Thermal Energy Domain $ Heat Transfer and Thermodynamic Concepts $ Lumped Element Modeling $ Ex: Self-Heating Resistor $ Other Dissipation Mechanisms
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2 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Analysis of Energy-Conserving Transducers : % Conservation of Energy % Principle of Virtual Work % Total work done by external forces creating displacement and deformation = internal stored energy in deformed and displaced state % Lossless Two-Port Networks % Analysis of Non Energy-Conserving Transducers % Dissipation % Thermal Energy Domain % Lumped Modeling of Dissipative Processes? Recall: Transducers
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3 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold Ref. Senturia, Microsystem Design, p. 271,272. Energy Transfer Between Energy Domains Dissipation
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4 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Reversible energy storage % Ideal compliance and inertances % Potential energy ! Kinetic energy % Irreversible energy storage : % Non-ideal (“real”) compliance and inertances % Dissipators Dissipation
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5 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold V I % Ex: Resistor % Joule Heating % P dissipation = VI = I 2 R % 1st and 3rd quadrant in V-I curve % Electrical energy converted to thermal energy V I Positive power dissipation Positive power dissipation (I) (II) (III) (IV) Ex: Electrical Resistor
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6 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold Ref. Senturia, p. 270. % Ex: Capacitor (charging) Stored energy on capacitor: Energy supplied by source: Energy dissipated in resistor: v C (t) Ex: Capacitor Charging/Discharging
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7 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Charging % 50% of energy supplied by source dissipated in resistor! % % Discharging % Vs set to 0 % Other 50% of energy dissipated in resistor % Even though the capacitor itself dissipates no energy, the process of charging and discharging dissipates energy v C (t) Ex: Capacitor Charging/Discharging Ref. Senturia, p. 270.
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8 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold Where does this energy go?? % Heat energy % Microscopic % Energy associated with specific motion of atoms and molecules and their degrees of freedom % Macroscopic % Manifests as temperature Thermal Energy Domain
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9 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold Heat capacity per unit mass [J/K-kg] % Definitions % Heat energy, Q [J] % Heat capacity, C [J/K] % Usually normalize by volume or mass % Heat energy per volume, q [J/m 3 ] Thermal Energy Domain For gases: Heat capacity per unit volume [J/K-m 3 ]
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10 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Heat obeys a continuity equation x x+ " x J Q (x,t) J Q (x+ " x,t) q(x,t) Illustration in 1-dimension Thermal Energy Domain J Q = heat flux through a surface [W/m 2 ] = volumetric heating from other energy domains [W/m 3 ] = power per unit volume of energy dissipated
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11 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Conduction % % Convection % % Radiation % Heat Transfer
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12 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold % Heat flow by conduction: Heat Flow
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13 Lecture 9 Thermodynamics EEL 5225, Fall 2010, David Arnold
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