Dissipation. Today: Dissipation. Thermodynamics. Thermal energy domain. Last lecture

Transcription

1 Last lecture Today: EEL5225: Principles of MEMS Transducers (Fall 2003) Instructor: Dr. Hui-Kai Xie MEMS Displays Dissipation Thermodynamics Dissipation Thermal energy domain Reading: Senturia, Chapter 11, p /29/ Lecture 26 by H.K. Xie 10/24/2003

2 First-order design review Time: 4:05pm-5pm, October 27, 2003 Place: Larsen 231 Presentation order: Electronic Nose by Hasan Rashid, Luis Jimenez, Jassica Bronson Mass flow sensor by Xavier Bellarmine, Uma Aghoram, Nicholas Lyn-Sue OCT 1 by Ankur Jain, Min Min, Shane Todd OCT 2 by Wonjae Chang, Anthony Kopa, Ken Lemp RF filter by Hyeopgoo Yeo, Maojiao He, Cem Tozeren, Mi-Young Jang Optical switch 1 by Heather Randell, James Brown, Kehuey Wu Optical switch 2 by Robert Taylor, Linquan Wang, Jungbae Kim, Sunk-Guk Lee Accelerometer by Deyou Fang, Diane Hickey, Hongwei Qu, Vijay Subramania Suggestions: 5 minutes presentation, 2 minutes for questions. ~6 slides Include introduction (background), design, modeling, simulation, process flow, packaging, plan me your presentation slides by 3pm Monday. Presentation archive All of the presentation slides and reports will be burned to CDs. You ll get one for free. 10/29/2003 2

3 Dissipative Processes Energy Transfer Between Non-Thermal Energy Domains and Thermal Energy Domain Ref. Senturia, Microsystem Design, p /29/2003 3

4 Dissipative Effects Dissipative Effects in Different Energy Domains: Ref. Senturia, Microsystem Design, p /29/2003 4

5 Electrical Resistance Passive resistor Voltage-Current relation, V=IR (Ohm s Law) neglecting nonlinear effects such as resistor selfheating and temperature dependence of resistance, R(T) Joule Heating, P dissipation =VI=I 2 R >0 1st and 3rd quadrant in VI space Electrical energy converted to thermal energy (II) + e V - negative power dissipation (III) Positive power dissipation e V fi R (I) e=e(f) Positive power dissipation negative power dissipation fi (IV) 10/29/2003 5

6 Charging a Capacitor Charging Capacitor is initially uncharged, v ( t = 0) = 0. The current is given by: t VS vc() t dvc() t. RC i = = C Solution gives charging transient: vc( t) = VS 1 e. R dt W Stored energy on capacitor 1 = CVS at end of transient. 2 * 2 C Energy supplied by source C v C (t) Ref. Senturia, Microsystem Design, p Energy dissipated in resistor 2 t V S RC WS = VSi() t dt = e dt = CV W S R = i () t Rdt = CVS R /29/2003 6

7 Charging a Capacitor Charging 50% of energy supplied by source dissipated in resistor! Thermal energy Energy converted to thermal energy Irreversible process v C (t) Ref. Senturia, Microsystem Design, p /29/2003 7

8 Thermodynamics 1st Law of Thermodynamics Conservation of Energy In the following formulation, focus on heat energy and work: du = dq dw where du =change in internal energy dq=differential heat energy entering system dw =differential work done by system on external world Case 1: Adiabatic process dq = 0 (No heat flows into or out of system) du = dw Case 2: Free expansion dw du = dq = 0 (No work done by system) 10/29/2003 8

9 Thermodynamics 2nd Law of Thermodynamics Entropy of an isolated system always increases *. Entropy, S, is a measure of disorder. 3rd Law of Thermodynamics Entropy of a pure perfect crystal approaches zero as the temperature approaches 0 K. Zeroth Law of Thermodynamics If two systems are in thermal equilibrium, then they must have the same temperature. 10/29/2003 9

10 Reversible vs Irreversible Processes Reversible process: Does not produce entropy Irreversible process: Produces entropy Randomization Disorder Uncertainty 10/29/ EEL5225: Principles of MEMS Transducers Ref. Reynolds (Fall and 2003) Perkins, Dr. Engineering Xie Thermodynamics, p.159.

11 Reversible vs Irreversible Processes Entropy, reversible process For a reversible cycle, Q = 0 T In the limit of infinitesimal temperature differences, dq dq = 0. The integrand,, is defined as the differential change T T in entropy, ds. Entropy, irreversible process Heat conduction is irreversible. What is the change in entropy? Cold T 2 Hot T 1 T 1 >T 2 10/29/

12 Heat Conduction: Irreversible Process Heat conduction To estimate the change in entropy, we Cold Hot construct a reversible process connecting the initial and final states. T 2 T 1 Entropy change for hot body= S = 1 Q T 1, m T 1 >T 2 Entropy change for cold body= S = 2 + Q T 2, m S final Sinit ial 1 S2 = S + > 0 T m T m Entropy increases for irreversible thermal conduction processes. Lukewarm 10/29/

13 Dissipation Today: Dissipation Thermodynamics Thermal energy domain 10/29/ Lecture 26 by H.K. Xie 10/24/2003

14 Variables of State Thermodynamic State Change in variable of state depends only on the initial and final states of the system and not on the path. Variables that satisfy this criteria: Pressure, p Volume, V Temperature, T Internal energy, U Enthalpy, H (=U+pV) Entropy, S (=Q/T) Variables that do not satisfy this criteria: Work, W Heat energy, Q 10/29/

15 Heat energy microscopic Thermal Energy Domain energy associated with specific motion of atoms and molecules and their degrees of freedom macroscopic Definitions related to temperature heat energy, Q [Joules] heat energy per volume, q=q/v [Joules/volume] heat capacity constant volume, C Q constant pressure, CP = T normalized heat capacity per unit mass 1 q C Cˆ V V ˆ V V Cm = = = ρm T V ρmv ρ C : Heat capacity per unit volume ˆV m 10/29/ Q T P

16 Continuity equation Thermal Energy Domain q + ijq = q t J sources 2 where Q =heat flux [Watts/m ] and q represent generation of sources heat inside material and couples thermal J Q (x,t) q(x,t) q source J Q (x+ x,t) domain to all other energy domains. x x+ x Note that q q T = = t T t ρ Cˆ m m T t Illustration in 1-dimension 10/29/

17 Heat conduction Heat Transfer driven by temperature difference = κ T J Q where κ =thermal conductivity [Watts/Kelvin-meter]>0 Convection complex process of heat conduction into fluid Radiation fundamental heat-transfer over space via photons between two bodies at temperatures, T 1 and T W JQ = σsbf12 ( T1 T2 ) where σsb = is 2 4 mk Stefan-Boltzman constant and 0<F < 1 takes into account the relative efficiency of radiant energy transfer. 10/29/

18 Heat Flow Equation Heat flow Heat flow equation Consider the divergence of the heat flux, ij = iκ T. Q Substituting into the continuity equation gives: q = iκ T + q sources t q T Using the relation for in terms of heat capacity and, t t ˆ T ρmcm = iκ T + q sources t If the thermal conductivity is constant, q ρ Cˆ T 1 T κ κ t α t 2 sources m m + = = T ρ Cˆ α = κ 1 m m 2 where [m /s] is the thermal diffusivity. 10/29/

19 Selected Thermal Coefficients Silicon Ref. Incropera and DeWitt, Fundamentals of Heat and Mass Transfer, p /29/