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Thermodynamics THERMODYNAMICS A GENERALLY GLOOMY SUBJECT THAT TELLS US THAT THE UNIVERSE IS RUNNING DOWN, EVERYTHING IS GETTING MORE DISORDERED AND GENERALLY GOING TO HELL IN A HANDBASKET James Trefil - NY Times THE LAWS OF THERMODYNAMICS THE THIRD OF THEM,THE SECOND LAW, WAS RECOGNIZED FIRST THE FIRST, THE ZEROTH LAW, WAS FORMULATED LAST THE FIRST LAW WAS SECOND THE THIRD LAW IS NOT REALLY A LAW P. Atkins ~ The Second Law Zero’th and third laws Temperature First law Conservation of energy THE SECOND LAW ENTROPY QUESTIONS DGm – Wh a t i s i t? Define T, S. What is thermodynamics? What are the laws of thermodynamics? THERMODYNAMICS Expresses relationships between the macroscopic properties of a system without regard to the underlying physical (i.e., molecular) structure. E.g., EQUATION OF STATE OF AN IDEAL GAS PV = nRT •Where does this come from? •What is the molecular machinery? ie. can we obtain this equation from a molecular theory ? •Can we also obtain equations of state for liquids and solutions? •How do we describe interactions? DEFINITIONS 1. VOLUME AND PRESSURE F Force F P = A Cross section area = A Volume V BOYLE’S LAW 1/V P V = constant EXPERIMENT 1 P ~ THEORY V (at constant T,n) P DEFINITIONS 2. TEMPERATURE - -What is it? Normal scales — °C, °F arbitrary Thermodynamic definition: - something that determines the direction heat will flow CHARLES LAW HEAT V ~ T (at constant n, P) V Is there an absolute If there is no heat flow, the scale of two bodies are at the same temperature ? temperature (zero’th law of thermodynamics) T O O -273 C 0 C Note: third law. Can’t get to absolute zero in a finite number of steps DEFINITIONS 3. The amount of stuff; n. • Don’t confuse mass and weight • Numbers of molecules - - large ! • Use moles (mol) as a unit (Latin - - massive heap) AVOGADRO’S PRINCIPLE 1 mol of particles = 12 V ~ n # of atoms in 12 gms of C 23 (constant T,P) 1 mol = 6.022 x 10 FINAL DEFINITIONS ENERGY AND ENTROPY Energy • Started with the concepts of HEAT and WORK • ~200 years ago these were considered to be different things and had different units WORK NEWTON Force x distance moved HEAT Caloric A weightless form of matter that flowed in and out of materials FINAL DEFINITIONS UNITED BY CONCEPT OF ENERGY, defined as the capacity to do work 1Joule = 1 kg m2 s-2 Joule - a wierd Manchester Brewer interested in the mechanical equivalent of heat Thermodynamics grew up around the question of the transformation of energy, particularly HEAT MECHANICAL WORK NOTE: It’s easy to turn mechanical work into heat Turning heat into mechanical work is much harder. Cannot turn 100% of the heat into work THERE IS A MISSING QUANTITY THE FIRST LAW Conservation of Energy dE = dQ - PdV Heat Q F dl = P dV (F dl = P Adl) dl ENTHALPY: HEAT SUPPLIED AT CONSTANT PRESSURE dQ p = d H H = E + P V GETTING WORK OUT OF HEAT WORK HEAT - easy HEAT WORK - harder CARNOT - Impossible to take heat at a certain temperature and convert it to work with no other changes in the system or the surroundings NO USEABLE WORK HOT USEABLE WORK COLD THE CONCEPT OF ENTROPY AROSE FROM THIS ANALYSIS __DQ DS = rev T ENTROPY - THEMODYNAMIC DEFINITION DQrev DS = T and From Carnot’s analysis DQ S > irrev D T W = – PdV Analogy Q = – TDS (note sign change - direction of Q) i.e., S is the quantity that defines the relationship between heat and temperature ENTROPY 16 TONS PE = mgh .. .. 16 . THUD !! . TONS . doesn't levitate ! . .. 16 . heat TONS . doesn't happen doesn't happen spontaneously spontaneously OTHER MANIFESTATIONS OF ENTROPY HOT COLD Happens spontaneously Also happens spontaneously ENERGY AND MATTER TEND TO DISPERSE CHAOTICALLY - THE SECOND LAW THE SECOND LAW OF THERMODYNAMICS AND FREE ENERGY For a process to occur spontaneously,S must increase; eg mixing DStot = DS sys + DSsurr But,if heat is released by the system S = - DQ sys = - DH sys D surr T T Define free energy D G = -TDS tot =DH -TDS FREE ENERGY DG ® advantage of using the free energy is that it contrives a way to relate overall changes to changes in the system alone WHY IS IT CALLED THE FREE ENERGY? – Because it is the maximum amount of non-expansion work that can be obtained from a system (T,P const) DG – DH ® heat tax! SUMMARY WE HAVE DISCUSSED THE ORIGIN OF THE THERMODYNAMIC EQUATIONS PV = nRT DGm = DHm - TDSm NOW WHAT? NEXT STEP INTRODUCE THE MOLECULES 1. From F = ma derive the gas laws and provide a molecular machinery 2. Show that by looking at averages and distributions of “mechanical” properties we can obtain S, G etc. FEYNMAN - LECTURES ON PHYSICS FEYNMAN - “If in a cataclysm all human knowledge was destroyed except one sentence that could be passed on to future generations – – – what would contain the most information in the fewest words ?” “ALL THINGS ARE MADE OF ATOMS – LITTLE PARTICLES THAT MOVE AROUND IN PERPETUAL MOTION, ATTRACTING EACH OTHER WHEN THEY ARE A LITTLE DISTANCE APART, BUT REPELLING UPON BEING SQUEEZED INTO ONE ANOTHER .” BASIC LAWS OF PARTICLES BASIC LAWS OF STUFF Mechanics (various forms) Thermodynamics Electricity + magnetism THE PROBLEM IS TO LINK THEM PRESSURE If there is no opposing force on the piston, each collision moves it a little bit. How much force, F, do we need to put on the piston to prevent movement? First: Remember P = F/A Second: How much force is imparted to the piston by the collisions ? .. d . (mx ) F = mx = dt i.e., WE NEED TO CALCULATE HOW MUCH MOMENTUM PER SEC IS DELIVERED BY THE COLLISIONS PRESSURE THIS IS EASY! a) Calculate momentum delivered by one collision b) Count # of collisions/sec v x Assume perfectly elastic conditions Then the particles have + mvx momentum before - mvx momentum after Change = mvx – (-mvx) = 2mvx PRESSURE Now calculate the # of collisions in time t FIRST: Define the number density n N = (# of particles/unit vol) V v x In a time t, only those particles that are close Enough and have sufficient v x velocity will hit the piston this doesn’t get x there in t v = x t Vol occupied by the molecules that will make it is v x t A The number hitting the piston = N vx t A # per sec = N vx A PRESSURE HENCE F = NvxA.2mvx F 2 P = = 2 Nm v x A a) All molecules don’t have the same v BUT x b) Some are moving away from the piston 1 2 S o r e p l a c e v 2 w i th v x 2 x 2 P = N m v x N o w 2 2 2 v x = v y = v z 2 1 2 2 2 2 v = v + v + v v x 3 x y z = 3 THE IDEAL GAS LAW- KINETIC THEORY 2 m v 2 HENCE P = N 3 2 2 n m v2 = 3 V 2 2 OR P V = n KE 3 COMPARED TO P V = n'R T IS n’ THE # OF MOLES ? IS KE ~ T ? Recall the thermodynamic definition TWO BODIES ARE AT THE SAME T IF THERE IS NO HEAT FLOW BETWEEN THEM. TEMPERATURE - KINETIC THEORY COLD HOT High density Low density Low v High v PISTON WHAT HAPPENS AT EQUILIBRIUM? •Forces balance FOR COLLISIONS OF •Atoms gain or lose energy depending on PAIRS OF MOLECULES wether the piston is moving towards them 2 2 or away from them during the collisions 1 m v = 1 m v 2 1 1 2 2 2 THEN – IF TWO GASES ARE AT THE SAME T, THE MEAN KE OF THE CENTER OF MASS MOTIONS ARE EQUAL. KINETIC THEORY - THE CONSTANTS k and R K E ~ T 1 m v 2 = 3 k T 2 2 2 P V = n 1 m v 2 = n k T 3 2 HENCE P V = n'R T At same T, P, V, n is a constant! Absolute scale of temp V z ero i s w h en 1 m v 2 = 0! T 2 IMPORTANT POINTS •A simple consideration of the motion of particles gives a fundamental understanding of P, T, the ideal gas law, absolute T and absolute zero, etc. •Can we stretch this approach and ultimately get a molecular interpretation of S , DG , etc.? THE DISTRIBUTION OF ENERGY AND MATTER All of the thermodynamic quantities we have dealt with so far deal with how much material is present and,on average,how fast the molecules are moving WHAT ABOUT a) The distribution of velocities? b) The distribution of molecules in space? i.e., THIS WILL LEAD TO A DESCRIPTION OF ENTROPY, DG etc. IN TERMS OF STATISTICAL ARGUMENTS EXAMPLE The distribution of molecules in the atmosphere ASSUMPTIONS Constant T ! No wind ! n P V = n k T o r P = Nk T ( N = V ) i.e., if we know P, we know n, if P is a constant BUT, in the atmosphere it varies h + dh P at (h + dh) must be less than P at h by an h Area A amount that is proportional to the weight of gas in Adh # of moles in Adh = NAdh Force Nadh = Area A EXAMPLE (cont.) h + dh h Area A Force Nadh = Area A Ph+dh - Ph = dP = - mgNdh P = NkT, or dP = kTdN dN mgN HENCE = - d h kT -m g h/k T -P E /k T N = No e = No e THIS IS A GENERAL RESULT BOLTZMANN’S LAW N ~ e -P E /k T -K E /k T SIMILARLY n > u ~ e STATISTICAL MECHANICS PROPERTIES OF PROPERTIES OF MOLECULES STUFF (Bulk Materials) Thermodynamics Classical mechanics How do we (P, T, V, G, S etc get from the Quantum mechanics + relationships molecules to between them) bulk properties ? Can bridge the “gap”by considering the average properties of all the particles of the system and the distribution of matter and energy.
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