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Internal Energy Energy – 1: Energy Heat Work Enthalpy Heat Capacity 1 © Prof. Zvi C. Koren 21.07.10 Thermodynamics = Thermo + Dynamics Laws of Thermodynaics: 0th, 1st, 2nd, and 3rd Laws Classical “Thermo”: empirical derivation of the laws (this course) Statistical “Thermo”: theoretical derivations via statistical quantum mechanics (if you “dare” to go there in the future …) 2 © Prof. Zvi C. Koren 21.07.10 Thermodynamics, is it an “easy” subject? From: http://www.journaloftheoretics.com/Articles/2-3/tane-pub.htm It is well known that while being very efficient in practice, the thermodynamic tool remains difficult to understand from the theoretical point of view. It is also well known that the difficulties encountered are not mathematical, but rather conceptual, and that they are perceived by those who have to learn thermodynamics as well as by those who have to teach it. The reality of the conceptual difficulty is openly and rapidly evocated rather than cancelled as a forbidden subject. One of the best examples is that given by the following opinion of the great physicist Arnold Sommerfeld about thermodynamics: "The first time I studied the subject, I thought I understood it except for a few minor points. The second time, I thought I didn't understand it except for a few minor points. The third time, I knew I didn't understand it, but it did not matter, since I could use it effectively." Arnold Johannes Wilhelm Sommerfeld Born: 5 Dec 1868 in Königsberg, Prussia (now Kaliningrad, Russia) 3 Died: 26 April 1951 in Munich, Germany © Prof. Zvi C. Koren 21.07.10 What can “Thermo” do for us? 1. What is the maximum amount of work that can be performed by an engine? 2. Which processes are spontaneous, and which need to be “kicked” into action? 3. Which battery system is the most efficient? Etc., etc., etc. … 4 © Prof. Zvi C. Koren 21.07.10 Thermodynamics = Thermo + Dynamics U U (or E) = Internal Energy What is meant by “internal” energy? U is connected to the important (relevant) processes. For example, if a chemical rxn occurs in a beaker, which is in a moving train, or on somebody’s head or on the ground (different potential energies due to height, position) what are we really interested in? Total Energy = Internal Energy + External Energy U (or E) f(position, velocity) 5 © Prof. Zvi C. Koren 21.07.10 Forms of Energy Kinetic Energy Potential Energy (Energy of Motion) (Energy of Position) Mechanical Gravitational (macroscopic objects in motion) (objects held in a certain position Thermal against the force of gravity) (submicroscopic motions of atoms, Electrostatic molecules, and ions) (positive and negative charges Electrical held in close proximity) (movement of electrons through a Chemical conductor) (energy attractions of electrons Radiant and nuclei in molecules) (electromagnetic radiation – photons – propagating through space) 6 © Prof. Zvi C. Koren 21.07.10 Interconversions of Kinetic Energy Mechanical Steam Stirrer Engine Generator Thermal Heater Electrical Sunlight Solar Heat Light Cell Lamp Bulb Radiant 7 © Prof. Zvi C. Koren 21.07.10 Interconversions of Kinetic & Potential Energies Kinetic Energy Potential Energy Car engine Static Mechanical cling Water Elevator wheel Gravitational Wood Thermal burning Falling Space meteor Electrostatic shuttle Electrical Battery Chemical Lightning Radiant 8 Fireworks © Prof. Zvi C. Koren 21.07.10 Energy Units James Prescott Joule (1818 - 1889) English physicist SI unit = Joule (J) 1 J = 1 kg·m2/s2 = 1 V·C = 1 Pa·m3 1 cal 4.184 J (exactly), cal = calorie 1 BTU = 1054.35 J, BTU = British Thermal Unit 1 kW·h = 3.6x106 J, kWh = kilowatt hour 1 L·atm = 101.325 J (exactly) 1 cal = energy needed to raise the temperature of 1 g of water by 1oC. 1 “dietary calorie” is 1 Cal (“big calorie”) = 1 kcal. Values & Units of R, Gas Constant: 0.0821 L·atm/mol·K 1.99 cal/mol·K 9 8.31 J/mol·K © Prof. Zvi C. Koren 21.07.10 System & Surroundings Open to everything Closed with respect NO thermal or, to matter, but there e.g., mechanical are thermal and, links to the outside e.g., mechanical world links to the outside world 10 © Prof. Zvi C. Koren 21.07.10 Diathermic vs. Adiabatic Walls T2 > T1 insulation 11 © Prof. Zvi C. Koren 21.07.10 State Functions properties that depend only on the state itself and not on the “history” of that state Examples State Variables: P, V, T, n Thermodynamic Properties: U (or E) = Internal Energy H = Enthalpy S = Entropy G = Gibbs Free Energy A = Helmholtz Free Energy Path Functions properties that depend on the process – the way the change is brought about Examples w (or W) = work (compression, expansion, stirring, electrical, …) q (or Q) = heat Heat is heat!!! But work could be many things! 12 © Prof. Zvi C. Koren 21.07.10 The Existence of Temperature & The Zeroth (0th) Law of Thermodynamics A Thermal Thermal Equilibrium Equilibrium B Thermal C Equilibrium That is, they’re all at the same T 13 © Prof. Zvi C. Koren 21.07.10 First Law of Thermodynamics Infinitesimal changes (differential form): dU = đq + đw Finite changes (integral form): U = q + w דיפרנציאל שלם )מסויים( = dx = exact differential đx = inexact differential (“dee-slash”) or x Benjamin Thompson Rumford (1753-1814) two methods of changing the energy of a system For example, as Lord Rumford noticed while working in a cannon factory, drilling into metal increased the temp, as if it was heated. Thus, w can have a similar affect as q in raising the U. The system does not “know” whether q and/or w were used to change its energy, U. We can tell, but the system is “blind”. Heat and work are equivalent ways of changing a system’s energy. The system is like a “bank”: It accepts deposits in either “currency”, but stores its reserves as internal energy. 14 © Prof. Zvi C. Koren 21.07.10 Schematic of Energy Changes in a System System w State 1 State 2 q גדַ לים מדידים: (P1,V1,T1,n1) (P2,V2,T2,n2) U1 U2 U = U2 - U1 תלוי במצבי הקצה )תחילי וסופי( U = q + w 15 © Prof. Zvi C. Koren 21.07.10 Notes about U = q + w : 1. First Law is for a closed system (closed to material, but open to q and w) 2. The equation is NOT any of the following: U = q + w or U = q + w U is a state function q and w are path functions 3. q & w are algebraic quantities (+ or –): A positive quantity is one that increases U, so: q = +, heat absorbed by system from surroundings: endothermic process –, heat released by system to surroundings: exothermic process w = +, work done on the system by the surroundings (e.g., compression) –, work done by the system on the surroundings (e.g., expansion) 4. While q & w are path-dependent, their sum is “amazingly” invariant. Other examples? (length of a vector, Hess’s Law, etc.) 16 © Prof. Zvi C. Koren 21.07.10 Back to First Law – Differential Form & The Meaning of dx and đx : dU = đq + đw dx (dU) đx (đq, đw) exact differential inexact differential infinitesimal CHANGE in x infinitesimal QUANTITY of x (between close states) đx = little bit of x: x1 đx1, etc. f f đx = x = x +x +x + ··· = x dx x f xi Δx j 1 2 3 i j1 (BIG x) i f f dx = x đx = x ii i đq đq đq 1 2 3 … State i State f qtotal Differential Form Integral Form dU = đq + đw dU = đq + đw U = q + w 17 © Prof. Zvi C. Koren 21.07.10 How can we tell whether a differential is exact (dz) or inexact (đz)? If “z” is a state function, where z=z(x,y), then: total partial differential derivative z z dz dx dy x y y x z z dz Mdx Ndy, M & N x y y x M z 2 z y y x yx order of x y x differentiation 2 N z z is irrelevant x x y xy y x y M N So, if dz Mdx Ndy and , then dz is an exact differential y x x y and z is a state function!!! (The reverse is also true.) 18 © Prof. Zvi C. Koren 21.07.10 More Two-Way Mathematical “Streets” For State & Path functions: If then dx is an exact differential x is a state function (property) then If đx is an inexact differential x is a path function (property) f dx constant x is a state function (property) i f đx f(integration path) x is a path function (property) i (x is a state function (property (מסלול סגור cycle integral) dx 0 (Why?) 19 Additional Problems on Exactness © Prof. Zvi C. Koren 21.07.10 Why is U a State Function? qa,wa;Ua 1 2 qb,wb;Ub U = q + w qa vs. qb, wa vs. wb, Ua vs. Ub ? Energy (and mass) cannot be created or destroyed: “Law of Conservation of Energy (and mass)” Why? Because!!! (Perpetual motion or perpetuum mobile machines do not exist.) Ua = –Ub, otherwise we WILL be able to create or destroy energy For an isolated sysytem (sys + surr), U is saved and dU = 0: dU = 0 U is a State Function 20 © Prof. Zvi C. Koren 21.07.10.
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