Thermodynamics. Temperature Scales Fahrenheit: t F. Thermal Expansion and Strss. Temperature and Thermal Equilibrium

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Abel Anthony
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herodynaics Fro the Greek theros eaning heat and dynais eaning power is a branch of physics that studies the effects of changes in teperature, pressure, and volue on physical systes at the acroscopic

1 herodynaics Fro the Greek theros eaning heat and dynais eaning power is a branch of physics that studies the effects of changes in teperature, pressure, and volue on physical systes at the acroscopic scale by analyzing the collective otion of their particles using statistics. eperature, pressure, and volue quantitatively define the state of a gas eperature, pressure, and volue are state variables We want to deterine the relationship (i.e., find soe equations) between these state variables and ore iportantly, relationships between changes in these state variables. eperature and heral Equilibriu he zeroth law of therodynaics: If two systes are each in theral equilibriu with a third, then they are in theral equilibriu with one another. If two theral systes are in theral equilibriu with one another, then they have the sae teperature. eperature is a way of deterining (easuring?) theral equilibriu wo systes have the sae teperature hey are in theral equilibriu wo systes have different teperatures he are NO in theral equilibriu Wikipedia: eperature Scales Fahrenheit: t F 3 at freezing point of water t F at boiling point Celsius: t C 0 at freezing point of water t C 00 at boiling point 9 5 ( F ) ( C) + 3 ( C) [ ( F ) 3] 5 9 Kelvin: t K 0 at absolute zero Δt K Δt C ( K ) ( C) ( C) ( K ) heral Expansion and Strss Solids expand when teperature increases; describe by coefficient of theral expansion (α): Δ α o Δ OR Δ oαδ For fluids, use coefficient of volue expansion (β) instead (as length is not well-defined): Δ β OR Δ oβδ o Δ Induced stress when the aterial does not freely expand or contract due to a teperature change he aterial is restricted in soe anner F oαδ σ E EαΔ o

Ideal Gas aw Using oles nr n nuber of oles R universal gas constant 8.35 J / (ol-k) Using olecules Nk N nuber of olecules k oltzann s constant.38 x 0-3 J / K his is called the Equation of State.

2 Ideal Gas aw Using oles nr n nuber of oles R universal gas constant 8.35 J / (ol-k) Using olecules Nk N nuber of olecules k oltzann s constant.38 x 0-3 J / K his is called the Equation of State. Why Ideal? Dilute, olue of Molecules is ~ Zero No ttractions etween Molecules eperature ust be in bsolute Units, K Real gases do not follow the ideal gas law precisely. owever, at low pressure and teperatures not too close to the liquefaction point, the ideal gas law is quite accurate and useful for real gases. Kinetic heory of Gases Connect icroscopic properties (kinetic energy and oentu) of olecules to acroscopic state properties of a gas (teperature and pressure). Nv N v ut K v and Nk K v k eperature is a easure of the average kinetic energy (internal energy?) of the gas. For constant volue, pressure increases directly proportional to an increase in average kinetic energy (teperature) ND an increase in the nuber of olecules. Molecular Speeds Since 3 3k K v k v v Distribution of olecular speeds, he Maxwell-oltzann distribution v 3 kt f ( v) πn v e Note 0 πk f ( v) dv N 8k v vf ( v) dv 0 N π 3k v rs v f ( v) dv 0 N v p rs df ( v) 0 dv v p k Real Gasses Reasonable ressure not too high Not near liquefaction point Why the breakdown? Near liquefaction Interolecular forces atter - Diagra Each line is at a constant teperature Solid Real, Dashed Ideal oint c is the critical point, curve C is critical tep.

hase Diagras riple oint is iportant as a reference standard What happens above the critical point?

Since the gas has a distribution of olecular speeds Soe olecules will be recaptured Condensation he gas will

apor ressure apor pressure explains boiling iquid teperature S teperature oiling occurs aw of partial

Relative uidity partial pressure of O R S of O 00% Dew oint: eperature at which unsaturated air will becoe

3 hase Diagras riple oint is iportant as a reference standard What happens above the critical point? apor ressure Since the liquid has a distribution of olecular speeds Soe olecules will escape Evaporation Since the gas has a distribution of olecular speeds Soe olecules will be recaptured Condensation he gas will exert a vapor pressure t equilibriu: saturated vapor pressure (S) his is teperature dependent. apor ressure apor pressure explains boiling iquid teperature S teperature oiling occurs aw of partial pressures he total pressure of a ixture of gasses the su of vapor pressure of the constituent gasses + + Relative uidity partial pressure of O R S of O 00% Dew oint: eperature at which unsaturated air will becoe saturated. Real Gasses - etter pproxiations Ideal Gas First Order Clausius Equation of State (EoS) nr nb Second Order an der Waals nr nb nr a ( / n) 3

Mean Free ath Molecular concentration ssue the other olecules are not oving, then

average distance between collisions d vδt l M NC N N π ( r) vδt πr If you account

the diffusing substance will ove a region of high concentration to a region of low

J C C D Δx J Rate of Diffusion D Diffusion Constant (gas dependent)

eat (Q) is the flow or transfer of energy fro one syste to another Often referred

teperature than the other eat will only flow fro the syste with the higher

4 Mean Free ath Molecular concentration ssue the other olecules are not oving, then the nuber of olecules in the cylinder is N N NC cyl π (r) vδt Mean Free ath is average distance between collisions d vδt l M NC N N π ( r) vδt πr If you account for the oveent of the other olecules l M N πr Rando Walk - Diffusion On average, the diffusing substance will ove a region of high concentration to a region of low concentration. Why? J C C D Δx J Rate of Diffusion D Diffusion Constant (gas dependent) Cross-Sectional rea eat What is heat? eat (Q) is the flow or transfer of energy fro one syste to another Often referred to as heat flow or heat transfer Requires that one syste ust be at a higher teperature than the other eat will only flow fro the syste with the higher teperature to the syste with the lower teperature eat will only flow fro the syste with the higher average internal energy to the syste with the lower average internal energy otal internal energy does not atter. Work W d

5 First aw of herodynaics When teperature changes, internal energy has changed ay happen through heat transfer or through echanical work First law is a stateent of conservation of energy Change in internal energy of syste equals the difference between the heat added to the syste and the work done by the syste ΔU Q W Differential for du dq dw eat added +, heat lost -, work done by syste +, work done on syste Internal Energy U is a state property Work W and heat Q are not ut work and heat are involved in therodynaic processes that change the state of the syste Molar Specific eats for Gasses Molar specific heats for gasses are different if heat is added at constant pressure vs. constant volue Q nc Δ Q nc Δ Isobaric, Δ 0 W Δ Q ΔU + Δ Isochoric, Δ 0 W 0 Q ΔU If the two processes result in the sae teperature change, ΔU is the sae. Q nc Δ nc Δ nrδ C C Q Δ R ypes of ransforations Isotheral, Δ 0 ΔU 0, W Q Work done by the syste equals the heat added to the syste nr W d d nr ln diabatic, Q 0 ΔU -W Work done by the syste lowers the internal energy of the syste by an equal aount eperature can change only if work is done. C W γ adiabatic constant, where γ γ C ypes of ransforations Isobaric, Δ 0 W Δ Work ressure*change in ol W d ΔU calculated fro st law Isochoric, Δ 0 W 0 ΔU Q d ( ) he change in internal energy of the syste equals the heat added 5

eat ransfer Conduction Δ Results fro olecular Δt interactions k Collisions?

electroagnetic radiation (waves) 0 e Does not require a ediu σ 5.

pushed slowly enough (quasistatically) that the syste reains in theral equilibriu (isotheral).

processes: Free expansion of a gas Melting of ice in warer liquid Frictional heating nything that is real ll real processes are irreversible!

Efficiency: Fraction of heat flow becoes echanical work: W Q Q Q e Q Q Q inial version of an engine has two reservoirs at different teperatures and, and follows a idealized

6 eat ransfer Conduction Δ Results fro olecular Δt interactions k Collisions? R-alue: Energy is transferred through interaction dq Convection dt Results fro the ass transfer of aterial hink fluid flow Radiation ΔQ eσ Energy transferred by Δt electroagnetic radiation (waves) 0 e Does not require a ediu σ Q l k l R k d dx 8 W / R K Net heat flow between two objects ( ) ΔQ eσ Δt Reversible & Irreversible rocesses Exaple of a Reversible rocess: Cylinder ust be pulled or pushed slowly enough (quasistatically) that the syste reains in theral equilibriu (isotheral). Change where syste is always in theral equilibriu: reversible process Change where syste is not always in theral equilibriu: irreversible process Exaples of irreversible processes: Free expansion of a gas Melting of ice in warer liquid Frictional heating nything that is real ll real processes are irreversible! eat Engine n engine is a device that cyclically transfors theral energy (heat?) into echanical energy (useful work). Efficiency: Fraction of heat flow becoes echanical work: W Q Q Q e Q Q Q inial version of an engine has two reservoirs at different teperatures and, and follows a idealized reversible cycle known as the Carnot cycle. Efficiency of the Carnot cycle Realistically, What is? What is a reasonable e C? W Q ec Q Q eat ups, Refrigerators, and ir Conditioners eat pups, refrigerators, and air conditions are engines run in reverse: Refrigerator and air conditions reove heat fro the cold reservoir and put it into the surroundings (hot reservoir), keeping the food/roo cold. heat pup takes energy fro the cold reservoir and puts it into a roo or house (hot reservoir), thereby waring it. In either case, energy ust be added! Work ust be perfored ON the syste! 6

eat ups and Refrigerators Since the (idealized) Carnot engine is the ost efficient heat engine, the Carnot refrigerator is the ost efficient refrigerator.

Coefficient of erforance: Q Q C W Q Q he Second aw of herodynaics here are any ways of expressing the second law of therodynaics; here are two: he Clausius for: It is ipossible to construct a cyclic

7 eat ups and Refrigerators Since the (idealized) Carnot engine is the ost efficient heat engine, the Carnot refrigerator is the ost efficient refrigerator. Coefficient of erforance: Q Q C W Q Q eat ups work siilarly but have a different objective, naely war the house. Coefficient of erforance: Q Q C W Q Q he Second aw of herodynaics here are any ways of expressing the second law of therodynaics; here are two: he Clausius for: It is ipossible to construct a cyclic engine whose only effect is to transfer theral energy fro a colder body to a hotter body. Spontaneous heat flow always goes fro the higherteperature body to the lower-teperature one. he Kelvin for: It is ipossible to construct a cyclic engine that converts theral energy fro a body into an equivalent aount of echanical work without a further change in its surroundings. heral energy cannot be entirely converted to work. 00% efficient engine is ipossible. hese definitions are incoplete! Entropy and the Second aw Entropy is a easure of disorder. here is soe controversy about this! he process of creating disorder (as well as order) increases entropy. Entropy is a easure of the energy unavailable to do work. It is a easure of the dispersal of energy. Energy is dispersed (used up?) in processes that create both order and disorder. Entropy and the Second aw he entropy of an isolated syste never decreases; spontaneous (irreversible) processes always increase entropy. ll the consequences of the second law of therodynaics follow fro the treatent of entropy as a easure of disorder. (?) Making engines that would convert echanical energy entirely to work would require entropy to decrease in isolated syste can t happen. Many failiar processes increase entropy shuffling cards, breaking eggs, and so on. We never see these processes spontaneously happening in reverse a ovie played backwards looks silly. his directionality is referred to as the arrow of tie. So, to what state is the universe heading? 7

Thermodynamics. Temperature Scales Fahrenheit: t F. Thermal Expansion and Stress. Temperature and Thermal Equilibrium

Thermodynamics. Temperature Scales Fahrenheit: t F. Thermal Expansion and Stress. Temperature and Thermal Equilibrium herodynaics Fro the Greek theros eaning heat and dynais eaning power is a branch of physics that studies the effects of changes in teperature, pressure, and volue on physical systes at the acroscopic scale