Review of classical thermodynamics

Transcription

1 Review of lassial thermodynamis Fundamental Laws, roperties and roesses () First Law - Energy Balane hermodynami funtions of state Internal energy, heat and work ypes of paths (isobari, isohori, isothermal, adiabati, yli) Enthalpy, heat apaity, heat of formation, phase transformations Calulation of enthalpy as a funtion of temperature Heats of reations and the Hess s law Reading: Chapters, 6., 6.4 of Gaskell or the same material in any other textbook on thermodynamis MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

2 hermodynami variables What are thermodynamis variables? here are two approahes to desribe properties and behavior of a material:. Mirosopi approah - to desribe the material in terms of mirosopi variables (positions, veloities, harges, et. of all partiles in the system). But there are too many partiles (N A = mol - ) and this approah in unpratial in most ases.. Classial (ontinuum) thermodynamis to desribe the material in terms of average quantities, or thermodynami variables, suh as temperature, internal energy, pressure, et. Statistial thermodynamis provides the onnetion between the lassial thermodynamis and the behavior of the mirosopi onstituents of matter (atoms and moleules). Although in this ourse we will fous on lassial thermodynamis, we will also onsider a few elements of statistial thermodynamis, in partiular in our disussion of heat apaity and entropy. What are state variables and funtions? System at equilibrium an be desribed by a number of thermodynami variables that are independent of the history of the system. Suh variables are alled state variables or state funtions depending on the ontext. We an desribe a system by a set of independent state variables and we an express other variables (state funtions) through this set of independent variables. For example, we an desribe ideal gas by and and use = R/ to define molar volume. For different appliations we an hoose different sets of independent variables that are the most onvenient. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

3 Intensive and extensive variables hermodynami variables Intensive properties independent of the size of the system, e.g.,. Extensive properties proportional to the quantity of material, e.g.,, C, H, S, G. + = + Example: if = = = then = + but = = We an also onsider derived intensive variables, e.g., Mass/olume or Energy/olume, that do not depend on the size of the system. Internal energy, heat, and work: not very rigorous definitions: It is impossible to give a rigorous definition of energy. (...in physis today, we have no knowledge of what energy is. - the Feynman Letures on hysis). hermodynamis laws do not define energy, thermodynamis is dealing with transfer of energy. In partiular, the st law of thermodynamis postulates the energy onservation. In thermodynamis of materials we usually do not onsider the kineti energy of the enter-of-mass motion of the system or gravitational energy (mgh), only internal energy, intrinsi to the body is onsidered. Internal energy is a sum of all potential and kineti energies in the system (not only of thermal/mehanial origin). hermodynamis is only dealing with hange of. he absolute value of is not defined by the laws of thermodynamis, but an arbitrary zero point is often hosen for onveniene. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

4 Early theory of heat: the alori fluid Frenh hemist Antoine-Laurent Lavoisier: he substane of heat is a subtle fluid alled alori the quantity of this substane is onstant throughout the universe, and it flows from warmer to older bodies. Based on observations that heat is onserved in some ases (e.g., when mixing hot and old water), Lavoisier proposed in 789 that heat is transferred by weightless, onserved fluid, named alori. Lavoisier's able of Simple Substanes (Elements) While we know that the alori ideas are invalid, we still say things like "heat flows to desribe the heat transfer MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

5 Heat generated from frition in annon boring proess, English physiist Benjamin hompson: Equivalene of heat and work I was struk with the very onsiderable degree of heat whih a brass gun aquires, in a short time, in being bored; [ ] A thorough investigating of these phenomena seemed even to bid fair to give a farther insight into the hidden nature of heat; and to enable us to form some reasonable onjetures respeting the existene, or non-existene, of an igneous fluid: a subjet on whih the opinions of philosophers have, in all ages, been muh divided. B. homson, hilosophial ransations, ol. XIII, 86, 798 Joule's experiment: the mehanial energy an be measured simultaneously with temperature (thermal energy). Joule found that the loss in mehanial energy is proportional to an inrease in temperature of the water and the amount of water used. the onstant or proportionality is 4.4 J/g ºC (modern data is 4.86 J/g ºC) Heat and work an independently produe idential hanges in the system. is not a good measure of heat but heat an be measured through work, and heat apaity an be determined. J.. Joule, On the existene of an equivalent relation between heat and the ordinary forms of mehanial power, hil. Mag. 7, 05, 845. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

6 Energy, heat, and work (ontinued) Heat is the energy being transferred to a system as a result of temperature differene (work-less transfer of internal energy). Work an be defined as the energy being transferred to a system as a result of a (generalized) fore ating over a (generalized) distane. Examples of work: Mehanial work done by fore F on a body moving from r to r along a ertain trajetory or path: r δw F dr F dr Work due to the volume expansion of a fluid or gas done against an external pressure. Eletri polarization work, where the generalized fore is the strength of the eletri field, E, and the generalized displaement is the polarization of the medium, D. δw E dd Magneti work, where the generalized fore is the strength of the magneti field, H, and the generalized displaement is the total magneti dipole moment, B. δw δw d H db r path integral Work and heat are both funtions of the path of the proess they are not state funtions. Systems never possess heat and work! Heat and work are transient phenomena desribe energy being transferred to/from the system. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

7 st Law onservation of energy in a thermodynami proess A state funtion, alled the internal energy, exists for any physial system and the hange in the internal energy during any proess is the sum of work done on/by the system and heat transferred to/from the system. = q w or in differential form: d = q - w internal energy (all potential and kineti energies). It is a state funtion depends only on thermodynami state of the system (e.g.,, & for a simple system). q energy added into the system as heat. ositive (+) when the system gains heat from outside (endothermi proess), negative (-) when heat flows out of the system (exothermi proess). w - work done by the system on its surroundings. ositive (+) when work is done by the system, and negative if work done on the system. If body does work, it expends energy and the internal energy of the body must derease. Note, that in some textbooks you will find a plus sign in front of w (work done on the body) or minus sign in front of q (heat flow out of the body). We use notation adapted in Gaskell. Example: pressure: w gas expands, mehanial work is done against an external ext d 0 - ooling by adiabati expansion MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

8 ypes of paths A simple one-omponent system an be desribed by,, and. hey are onneted by equation of state, e.g. =(,). herefore, two independent variables desribe the system and define the state funtions, e.g. = (,). Let s onsider proesses when one of the two independent variables is fixed. = onst isohori proess No work is done (w = d = 0) and the st law takes form: d = q or = q (internal energy an be hanged only by heat exhange) = onst isobari proess w d d and the st law takes form: = q p ( ) or ( + ) ( + ) = q p q p is heat added at onstant pressure. H = + enthalpy - state funtion (sine,, are state funtions) H H = H = q p hange in enthalpy equals to heat added to the system at onstant pressure MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

9 = onst isothermal proess Example: ideal gas ypes of paths (ontinued) d = 0, therefore, d = q - w = 0 (internal energy of an ideal gas is a funtion only of ). Work done depends on the path, i.e. how the external pressure is hanging during the transformation. For example: Free expansion (no external pressure): w = 0 Reversible isothermal expansion ( ext = gas at all times) (reversible proess system is always at equilibrium) q = w = d = Rd/ per mole of gas Integration between states and gives q = w =R ln( / ) = R ln( / ) Work done by the system = heat absorbed by the system Q = 0 - adiabati proess = -w - no heat exhange, the internal energy an be hanged only by work. Real proesses are often omplex,, and all are hanging. In this ase state funtions an be alulated by breaking proess into a series of reversible isothermal, isobari, or isohori proesses that bring system to orret final state. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

10 Surfae of a ure Substane MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

11 ypes of thermodynami systems Isolated system No energy and no matter an pass through the boundaries of the system. Closed system Energy an pass through the boundaries (as heat and/or work), but matter annot. Adiabati system No heat an pass through the boundary (neither an matter that an arry heat) ideal thermos. Work an be performed on or by the system. surroundings work heat surroundings work surroundings Open system Both energy and matter may pass through the boundaries. work heat matter surroundings An alternative formulation of the st law of thermodynamis: he work done on a system during an adiabati proess is a state funtion and numerially equal to the hange in internal energy of the system. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

12 Heat Capaity he heat apaity, C, of a system is the ratio of the heat added to the system, or withdrawn from the system, to the resultant hange in the temperature: C = q/ = q/d [J/deg] his definition is only valid in the absene of phase transitions sually C is given as speifi heat apaity,, per gram or per mol New state of the system is not defined by only, need to speify or onstrain seond variable: C C q d q d - heat apaity at onstant volume - heat apaity at onstant pressure he fat that q is not a state funtion and depends on the path is refleted in the dependene of the heat apaity on the path, p v (note that small is used for the derived intensive quantity, per mass, per volume, or per mole, versus apital C for the extensive quantity. For a system ontaining n moles C p = n p and C v = n v where p and v are molar values). and an be measured experimentally isobari proess: isohori proess: dh = q = d d = q = d H and an be alulated from and MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

13 MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei v vs. p If material is allowed to expand during heating, how this affets its heat apaity? v d δq p H d δq Differentiation with respet to at onstant gives v d d d,, sine therefore v work of expansion at onstant due to the temperature inrease by d work of expansion against internal ohesive fores due to the temperature inrease by d

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15 Calulation of enthalpy from heat apaity For = onst, dh = d and integration gives: H H dh H H d H H d Example: Let us find enthalpy for opper at 500 K. 4.4 Jmol - K - for opper at atm. From the st law an only alulate the differene H - need a referene enthalpy. Enthalpy at atm and K is alled enthalpy of formation, H. For pure elements in their equilibrium states H = H500 H d 0 4.4d 4.9kJ/mol Enthalpy of substanes other than pure elements an also be alulated. he enthalpy of a ompound at K = standard heat of formation of the substane from the elements. Example: For oxidation of opper at 5 C: CuO CuO Cu O H H H H Cu solid + ½ O gas = CuO solid H CuO -56. kj/mol he reation is exothermi heat and/or work are produed MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

16 Calulation of enthalpy from heat apaity (ontinued) In general, heat apaity is a funtion of temperature. For example, for alumina, Al O 3, the temperature dependene an be desribed by p = Jmol - K - in the range -35 K H AlO AlO3 H d kj/mol d kj/mol he standard heat of formation, Al O H 3, and heat apaity, p (), are measured experimentally and an be found in themohemial tables, e.g. at or at the end of Gaskell s textbook In most ases, thermal treatment of materials is arried out under atmospheri pressure and no work other than work of expansion against the atmosphere is produed. Enthalpy hange is used to desribe suh proesses. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

17 Enthalpy and phase transformations If the system undergoes a phase transformation (or a hemial reation) then the enthalpy hange due to the phase hange, H trans, has to be inluded into total enthalpy hange. Also, different phases an have different heat apaities, p (). For example, let s find enthalpy for opper at 000 K. solid = Jmol - K - in the solid state for = K (this formula for p () is given at Sine this time we are onsidering a wide range of temperatures, we should aount for the temperature dependene of p ( p 4 Jmol - K - at K, 6 Jmol - K - at 500K, 33 Jmol - K - at 358K) liquid = 3.8 Jmol - K - in the liquid state (nearly independent on ) H m = kj mol - latent heat of melting always positive solid liquid H 000 H p d H m p d kJ - mol MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

18 Heat of formation and phase transformations If the temperature of interest is higher than the melting temperatures for both the metal and its oxide, the enthalpy hange for M liquid + ½ O gas = MO liquid is then H H M m MO,solid p M,solid p O p,gas d H M m MO m M m MO,solid p M,liquid p O p,gas d H MO m MO m MO,liquid p M,liquid p O p,gas d MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei Gaskell, Chapter 6.4

19 Heats of Reations Hess s Law Heat absorbed or released in a given hemial reation ourring under onstant pressure onditions is the same weather the proess ours in one or several steps (Hess, 840). Example: C (graphite) + O (gas) = CO (gas) Q = kj mol - C (graphite) + ½ O (gas) = CO (gas) Q = kj mol - CO (gas) + ½ O (gas) = CO (gas) Q = -83. kj mol - otal: kj mol - Hess s Law allows one to alulate Q for reations that is hard to measure resene of atalysts hange the ativation energy of reation but not the net heat of reation. he Hess s law is just a onsequene of the st law of thermodynamis: for = onst, H = Q. Sine H is a state funtion, total heat is independent of path. MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

20 Calulation of heat of transition from heats of reations Let s find if an allotropi transition from diamond to graphite under ambient onditions results in the release or absorption of heat. C (graphite) + O (gas) = CO (gas) H = kj mol - C (diamond) + O (gas) = CO (gas) H = kj mol - hen for reation C (diamond) C (graphite) H = = -.9 kj mol - ransition of diamond to graphite is an exothermi reation Graphitization of a surfae region of diamond at elevated temperature Figure from a omputer simulation MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei

21 Summary Make sure you understand language and onepts: hermodynami funtions of state (no dependene on path/history): volume temperature pressure omposition internal energy enthalpy Heat and work are not state funtions ypes of paths isobari isohori isothermal adiabati ypes of systems open losed isolated adiabati Calulation of enthalpy as a funtion of temperature Enthalpy and phase transformations Heat of formation Standard heat of formation Heats of reations and the Hess s law MSE 3050, hermodynamis and Kinetis of Materials, Leonid Zhigilei