Announcements. HW 3B due today (now!) HW 4A (Wed), 4B (Mon) HW5A (ch22) & 5A (fluids) QUIZ 4 Thursday

Size: px

Start display at page:

Download "Announcements. HW 3B due today (now!) HW 4A (Wed), 4B (Mon) HW5A (ch22) & 5A (fluids) QUIZ 4 Thursday"

David Hodge
5 years ago
Views:

1 Announcements W 3B due today (now!) W 4A (Wed), 4B (Mon) posted W5A (ch) & 5A (fluids) QUIZ 4 hursday Mirrors, lenses, & thermo (9 & 0) QUIZ 5 Next Wednesday (thermo) Final one week from FRIDAY! about special arrangements ASAP QUIZ 3: Average: 6.%+/- 7.%

2 Physics C hermodynamics he study of heat, heat flow, temperature, equilibrium, energy, work, engines, and entropy.

3 hermodynamics Macroscopic vs microscopic hermo<stat Mech, inconsistencies QM he engine of our society eat engines Many microscopic states correspond to one macroscopic state Cars, planes, trains, any other smoke-emitting, fuel burning engine Chemistry Industrial, medical Biology Osmosis, cellular work

What is heat? eat is a form of energy Random energy, usually random kinetic energy Particles fly in random directions Other random forms possible (e.g., spin orientation) Can sometimes be used to do useful work But heat is not as efficient as ordered energy http://www.

4 What is heat? eat is a form of energy Random energy, usually random kinetic energy Particles fly in random directions Other random forms possible (e.g., spin orientation) Can sometimes be used to do useful work But heat is not as efficient as ordered energy

5 temperat ture eat C Ideal Gas emperature (constant volume) pressure What is temperature? A driving force behind heat (energy) flow ard to give a precise definition (thermodynamic eq) Can use the gas-thermometer definition: emperature is what is measured by a gas thermometer Constant volume gas thermometer gives best results gas thermometers fail at low P temperatures (< ~00 K) 3 P3 0 K absolute zero riple point (unique) K 73.6 P P 3

emperature scales Kelvin Used in science, and especially thermodynamics Ice: 73.5 K Steam: 373.

6 emperature scales Kelvin Used in science, and especially thermodynamics Ice: 73.5 K Steam: K (00 deg spread) Absolute zero: 0 K No degrees: they re kelvins(lower case) Centigrade, or Celsius Used in most technological cultures Ice: 0 C, Steam: 00 C (00 deg spread) 73.5 C K Fahrenheit Only used by backward societies Ice: 3 F,Steam: F (80 deg spread) 9 F 5 C + 3

7 hermal equilibrium W W wo systems are in thermal equilibrium when no energy spontaneously flows between them It s a dynamic equilibrium with small fluctuations If A is in equilibrium with B, and B with C, then A will be in equilibrium with C. he zeroth law of thermodynamics Nota statement of speed or time (Converse not true) A B C B C A B A C

8 Specific eat & eat capacity eat capacity, capital C eat per unit Kelvin (depends on m) Q C Specific heat, c eat per unit mass, per Kelvin (or per C) Q mc Water: Ice: Aluminum: Steel: ~4000 J/kg-K ( cal/g-k) ~000 J/kg-K ~900 J/kg-K ~500 J/kg-K Large bodies of water (ie ocean) have LARGE heat capacity moderate all year

9 Equilibrium emperature eat flows from hot to cold until thermodynamic equilibrium eat C mc + mc 0 mc ( ) mc( ) eq C eq C eq eq

10 eat flow: a statement about speed (and therefore time) Units? 3 common mechanisms: Conduction(direct physical contact) Convection (fluid flow) Radiation (EM waves) dq dt C

11 Conduction: heat flow through collisions kis the thermal conductivity, such that dq dt ka d dx Pans with copper bottom: igh thermal conductivity insulation [k] J/s-m-K W/m-K Air: ~0.06 Concrete: ~ Copper: ~400 Fiberglass: ~0.04 C C

12 Conduction several layers eat does not accumulate heat flow must be equal: k A ( ) ( ) x hermal resistance: k A 3 x R x ka (k property of material, R property of particular piece of material) R R factor: R RA x k 3 3 k k Δx Δx

Convection: hot fluids rise, cold fluids fall ransport of heat carried by a fluid during its motion Very complicated, due to complexity of fluid flow which is

13 Convection: hot fluids rise, cold fluids fall ransport of heat carried by a fluid during its motion Very complicated, due to complexity of fluid flow which is often turbulent Large amount of random energy Can increase heat flow by orders of magnitude Morning after cold, calm night, just above ground drops as sun rises

Evacuated walls, reflective coating 8 4 σ 5.

14 hermal Radiation: heat transfer by EM waves Stefan-Boltzmann Law P or where eaσ e emissivity 4 Evacuated walls, reflective coating 8 4 σ W/m K 0 perfectly reflecting perfectly black eat flow in vacuum

15 hermal balance vs. thermal equilibrium Equilibrium items at same temperature Balance constant temperature difference in out Greenhouse gases absorb IR, making Earth s surface higher than in their absence, heat flow green house

16 Ideal gas: k J K 3 N A # / mol R J K Ideal Gas Pascal Constant particle #: P V PV Constant : P V P V PV Nk Cubic meters Particles (atoms, molecules,etc) moles nr Kelvin

17 hermal behavior of matter: Ideal Gases Kinetic theory of ideal gases: Large # of identical point particles No interparticle forces (KE only) Velocities randomly distributed Collisions with walls are elastic Momentum change: ime b/n collisions: Force: Pressure: P F N p t F A mv L v ix xi mn V p i mv xi t L x v mv L i v xi ix mn 3V v Pressure avgf/a a look at a collision Length, L Surface area A Length, L Surface area A wall

18 Pressure: Ideal Gas (continued) P mn 3V PV N m v 3 v Nk measures average KE associated w/ random collisions m v k hermal speed (root mean square): 3 3k v th m Average speed increases with gases at same, different m diff rms speed

19 Speed distribution Random motion distribution of speeds Maxwell-Boltzmann distribution: N m πk mv k ( v) dv 4πN v e dv Number of molecules w/ speed vto v+dv Increase in : igher peak speed Wider distribution igher thermal speed 3

20 Real Gases Ideal assumes: noninteracting, point particles Real: Induced dipole interactions (alters pressure) ake up finite space (alters volume) Van der Waals equation: n a P + V ( V nb) nr where a and b depend on type of gas

21 Phase Changes Gas liquid-solid Requires heat added, taken away ice cubes + ice, f? 0 degrees Celsius until ice melts Latent heat (J/kg): Q Lm eat of transformation only heat associated with phase change Recall, Q mc

22 eat of fusion and heat of vaporization Recall heat capacity of water: c cal/g-k 4.84 J/g-K Q 334 J/g It takes heatto melt something, even though there is no temperature change E.g., ice water: L f 80 cal/g 334 J/g It takes heatto vaporize something, even though there is no temperature change E.g., water steam: L v 60 J/g Q 60 J/g

23 hermal Expansion Fractional change in volume: Coefficient of volume expansion β V V Fractional change in length: Coefficient of linear expansion hermal expansion of water: Ice floats L L α ( β 3α ) Pressure increase melts ice

24 Announcements Key for 3B uploaded W 4A (Wed), 4B (Mon) posted W5A (ch) & 5A (fluids) QUIZ 4 hursday Mirrors, lenses, & thermo (9 & 0) QUIZ 5 Next Wednesday (thermo) Final one week from FRIDAY! about special arrangements ASAP Check your grades!!!!

25 Review 0 th law: A is in thermal eqw/b, A is in thermal eqw/c; then B is in thermal eqw/c emperature drives heat (energy) flow Q mc Conduction, convection, and radiation dq dt d ka dx eσa hermal balance in out Ideal gases PV Nk nr 3k Boltzmann distribution v th m Latent heat of transformation Q Lm Coefficient of linear/volume expansion P 4 α β L L V V

26 First Law of thermodynamics: (dynamic) conservation of energy Internal energy, U, increases when we add heat Internal energy decreases when we take out work U Q W internal in energy net out positive heat is in positive work is out unless otherwise noted du dt dq dt dw dt Q in > 0 Q net Q in - Q waste Q waste <0 internal energy, U W > 0

27 Reversible vsirreversible Processes Reversible Quasi-static: slow Reservoir and sample in eq PV diagram Irreversible Sudden change Pressure, emperature not well defined No PV diagram First law holds for both U Qnet W

28 Examples of Work dw F dx linear force-distance A surface area dw dw σ da P dv surface tension pressure-volume work dx dw dw τ dθ db rotational work magnetic work dv A dx dw q dφ electric work Work energy theorem, e.g.: Also, radiation (light) Sound W F dx PA dx P dv V V

29 hermodynamic Processes Isothermal: Δ0, (ΔU0) U Qnet W Q W nr V Isochoric: ΔV0 (W0) Q U nc Isobaric: ΔP0, WPΔV: Q V P W PdV dv nr ln( V V ) V Adiabatic: Q0; γ PV C V 3 U KE Nk V V U Qnet W nr V U ΔUnC vδ n (Ideal) ALWAYS for ideal gas U + W nc + P V nc CP CV + R U Q W net P 0 V 0 γ C P C V γ V W V U W γ γ 0V 0 U nc nr V P P decreases faster for Q0 than Δ0

30 Work Area under PV diagram Cyclic processes Area inside closed cycle CCW, W<0 CW, W>0 W>0 W<0

31 Specific eat: Ideal vsdiatomic Recall thermal speed per molecule: Internal energy (ideal gas): Specific heat: Adiabatic exponent: U 3 Nk 3 mv nr U 3 C V R n CP CV + R 5 3 γ R R C C V V k For diatomic gases: C V R γ C diatomic V C ideal V γ 3 5 R R degrees of freedom: 3 translational (v x, v y, v z ) rotational (rotation about axes perpendicular to separation) 3 degrees of freedom (v x, v y, v z )

32 Equipartitionheorem When a system is in thermal equilibrium, the average energy per molecule is ½k for each degree of freedom 3 5 U ideal Nk U diatomic Nk

33 Laws of thermodynamics 0 th law: AB, BC; AC st law: U Q W internal in energy net nd law: Systems spontaneously evolve to macro-states of higher likelihood Implies systems evolve towardthermal equilibrium Not away from it 3 rd law: 0K out

$engines can only use a fraction of the heat from the high temperature reservoir Perfect engine W > 0 Real engine ΔU0 Efficiency: e W/Q e(q -Q C )/Q e-q C /Q Q C <Q W > 0$

34 nd Law and eat Engines It is impossible to construct a heat engine operating in a cycle that extracts heat from a reservoir and delivers an equal amount of work Real engines can only use a fraction of the heat from the high temperature reservoir Perfect engine W > 0 Real engine ΔU0 Efficiency: e W/Q e(q -Q C )/Q e-q C /Q Q C <Q W > 0 Q Q

35 Carnot Engine (max efficiency) eat rejected, not absorbed Reversible, cyclic Q Q C Q Q nr nr C C C ln ln ln ln ( V V ) b a ( V V ) d ( Vc Vd ) ( V V ) b a c e Q Q C V V V a V d V b V c γ CV c V b Vd γ γ V V γ b a C V d Q C C C e Q a c (Kelvin)

36 Carnot engine Engine: extract some useful work from internal energy Efficiency: W e Q Refrigerator: opposite of engine ΔU0 U Q W internal in energy C net out ΔU0 Actual efficiency: e dw dq Waste: dq dt dq dt dw dt dt ( dm dt) c C W Q dq C dt dt

expansion cold valve Q in air to be (Q cooled C ) Q out (Q ) heat exchanger (radiator) high pressure low

37 Energy flow in refrigerator (or heat pump) ΔU 0 Q net W W W in < 0 Q net Q in Q out < 0 Ideal: Carnot cycle in reverse (takes in W and transfers heat from colder reservoir to hotter reservoir) e W Q Q ΔU0 C Q Q C warm expansion cold valve Q in air to be (Q cooled C ) Q out (Q ) heat exchanger (radiator) high pressure low pressure heat exchanger (radiator) outside air cool hot W in compressor motor refrigerant, deliberately a non-ideal gas

38 ΔU 0 Q net W COPs: enforcing the ( st ) law coefficient of performance, COP want pay Same definition as efficiency But, COP can be > So we don t call it efficiency W W in Q net Q in Q out ΔU0 C For air conditioner, COP AC Q in /W in Q C /W in ypically 4 for a good AC he book is wrong on COP for heat-pump COP P Q / W in Which is ( + Q in / W in ) ΔU0

39 Entropy Units of J/K Entropy is really a measure of multiplicity not disorder Multiplicity, g,is # of microstates consistent with a given macro-state Nonetheless, in some cases, our aesthetic sense of disorder agrees with multiplicity But sometimes not Aesthetics are subjective; entropy is not.

40 Entropy (continued) Recall for carnotcycle: Rearrange: Q Generalize for any reversible cycle: Continuum limit C C Q + 0 dq 0 Q C Q C Q Quantity that does not change when taken over a cyclic path: S Entropy (character of state) dq Path independent (increases for irreversible) 0

41 Entropy (continued) nd law (restated): entropy of a closed system can never decrease (at best stays constant) No heat transfer no entropy change? (irreversible) adiabatic free expansion U Q W S P V in out Energy unavailable for work E unavailable min S Coldest available to system If entropy increases by ΔS, some energy becomes unavailable for work Consider reversible process that takes V V (isothermal expansion)

42 Quality of Energy systems with identical ammountsof internal energy, system with less entropy contains higher energy quality S S (more ability to do work) S <S

43 Quiz 4 Review Ch 36, 9 & 0 Lenses, mirrors: + o i Converging (f>0) diverging (f<0) Real image (i>0) virtual (i<0) Inverted (M<0) upright (M>0) Rules for image formation from ray diagrams f M i o R f Incident parallel refracted toward/away from the focal point Incident through focal point refracted (reflected) parallel to the symmetry axis Incident on center: reflected symmetrically or passes straight through lens, unrefracted

44 Quiz 4 Review Refraction at a curved surface: Lensmaker s formula: Convex to object, R i >0 (thicker on the edges, f<0) R n n i n o n + ( ) R R n n f ( ) R R n f Simple magnifier: Compound microscope: Refracting telescope: f cm m 5 α β f e f L M 5 0 f e f m 0

45 emperature scales P P 3 Quiz 4 Review 9 c F C eat energy transfer due to Δ, transformations: Q mc C eat transfer: conduction radiation Ideal gases hermal speed Boltzmann P σ hermal expansion N Q ml ka x e A σ W / m K PV Nk v th 3k m m πk 3 nr m v 3 k mv k ( v) v 4πN v e v α L L β V V R 3 k.38 0 J / K R 8.34J / K mole N A R x ka R RA x k n a P + V ( V nb) nr

18.13 Review & Summary

5/2/10 10:04 PM Print this page 18.13 Review & Summary Temperature; Thermometers Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains