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The Laws of Thermodynamics Macroscopic Physics: Classical Equilibrium Thermodynamics! First: 3 Slides of Some Results from Microscopic Statistical Physics Fundamental Statistical Physics Concept # of accessible microstates for a macroscopic system with huge particle number N + huge number f degrees of freedom. • Suppose we know that the energy of the system is in the range E to E + δE. Define: Ω(E) ≡ Number of accessible micro states for this system. • It can be shown that Ω(E) varies with E approximately as Ω(E) Ef • This is the starting point for the connection between microscopic physics & classical thermodynamics! Ω(E) Ef • Specifically, all macroscopic thermodynamic functions can be derived from Ω(E)! d Entropy S: S kB ln E Temperature T: Also Define: 1 S E N ,V T ln E E N ,V Ω(E) S kB ln E f E 1 S E N ,V T ln E E N ,V • So, the connection between & the absolute temperature T is clearly: h [1/(kBT)] • Also, equations of state can be derived from Ω(E). The Zeroth Law of Thermodynamics • Definition: If 2 systems are in thermal equilibrium, their absolute temperatures are equal! (Isn’t this obvious)?? “If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.” This allows the design & the use of Thermometers! The First Law of Thermodynamics • Consider a system A1 interacting (exchanging energy) with a system A2 Heat absorbed by system A1 Q = ∆Ē + W Work done by system A1 Change in internal energy ofL system A1 Physics: Conservation of Total Energy!! So The Physical Meaning of the 1st Law of Thermodynamics is that Total Energy is Conserved The First Law of Thermodynamics For Infinitesimal, Quasi-Static Processes Heat absorbed by system A1 đQ = dĒ + đW Change in internal energy of system A1 Work done by system A1 T This is another form of Conservation of Total Energy!! So The Physical Meaning of the 1st Law of Thermodynamics is still that Total Energy is Conserved Rudolf Clausius’ statement of the 1st Law of Thermodynamics “Energy can neither be created nor destroyed. It can only be changed from one form to another.” Rudolf Clausius (1850) The Physical Meaning of the 1st Law of Thermodynamics Conservation of Total Energy!!!! However, it says nothing about The Direction of Energy Transfer! The 2nd Law of Thermodynamics: “The entropy of an isolated system increases in any irreversible process & unaltered in any reversible process.” • This is sometimes called The Principle of Increasing Entropy DS 0 Change in the system entropy It gives the Preferred (natural) Direction of Energy Transfer • It thus determines whether a process can occur or not. The 2nd Law of Thermodynamics: “The entropy of an isolated system never decreases”. •Mathematically, this means that in Change in Entropy any process ΔS ≥ 0 or, at equilibrium, S → Smax For (idealized) reversible processes only, ΔS = 0, dS = đQ/T. Examples of Irreversible (real) processes: • Temperature Equalization, • Mixing of Gases, • Conversion of Macroscopic (ordered) KE to Thermal (random) KE • The last 2 cases are examples of the Association of Entropy with Disorder. General Features of the Entropy S General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. • It is a quantitative measure of the disorder in a system. General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. • It is a quantitative measure of the disorder in a system. • It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy. General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. • It is a quantitative measure of the disorder in a system. • It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy. • ΔS may be negative for a portion of a composite system. General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. • It is a quantitative measure of the disorder in a system. • It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy. • ΔS may be negative for a portion of a composite system. • An increase in S does not require an increase in temperature. For example, the mixing of gases at the same temperature, or in the melting of a solid at the melting point. General Features of the Entropy S • It is a state function, so that ΔS between given macrostates is independent of the path. • It is a quantitative measure of the disorder in a system. • It gives a criterion for the direction of a process, since an isolated system will reach a state of maximum entropy. • ΔS may be negative for a portion of a composite system. • An increase in S does not require an increase in temperature. For example, the mixing of gases at the same temperature, or in the melting of a solid at the melting point. • An increase in temperature does not necessarily imply an increase in S. For example, in the adiabatic compression of a gas. Some Historical Comments • Much of the early thermodynamics development was driven by practical (Engineering) considerations. For example, building heat engines & refrigerators. • So, the original statements of the Second Law of Thermodynamics may sound very different than those just mentioned. Various Statements of the nd 2 Law of Thermodynamics: 1. “No series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work.” That is There are NO perfect engines! Two of Rudolf Clausius’ statements of the 2nd Law of Thermodynamics 2.“It will arouse changes while the heat transfers from a low temperature object to a high temperature object.” Two of Rudolf Clausius’ statements of the 2nd Law of Thermodynamics 2.“It will arouse changes while the heat transfers from a low temperature object to a high temperature object.” 3.“It is impossible to devise an engine which, working in a cycle, shall produce no effect other than the transfer of heat from a colder to a hotter body.” Two more Rudolf Clausius’ statements of the 2nd Law of Thermodynamics 4. “During real physical processes, the entropy of an isolated system always increases. In the state of equilibrium the entropy attains its maximum value.” Two more Rudolf Clausius’ statements of the 2nd Law of Thermodynamics 4. “During real physical processes, the entropy of an isolated system always increases. In the state of equilibrium the entropy attains its maximum value.” 5. “It is impossible to design a cyclic device that raises heat from a lower temperature to a higher temperature without affecting its surroundings.” Two more Rudolf Clausius’ statements of the 2nd Law of Thermodynamics 4. “During real physical processes, the entropy of an isolated system always increases. In the state of equilibrium the entropy attains its maximum value.” 5. “It is impossible to design a cyclic device that raises heat from a lower temperature to a higher temperature without affecting its surroundings.” • Stated a different way: Raising heat from a lower temperature to higher temperature always requires either doing work on or exhausting heat to the environment. Two of Lord Kelvin’s (William Thompson’s) statements of the 2nd Law of Thermodynamics 6. “It will arouse other changes while the heat from the single thermal source is taken out & is totally changed into work.” Two of Lord Kelvin’s (William Thompson’s) statements of the 2nd Law of Thermodynamics 6. “It will arouse other changes while the heat from the single thermal source is taken out & is totally changed into work.” 7. “A process whose effect is the complete conversion of heat into work cannot occur.” Two of Kelvin’s & Planck’s joint statements of the 2nd Law of Thermodynamics 8. “It is impossible to extract an Lord Kelvin amount of heat QH from a hot reservoir and use it ALL to do work W. Some amount of heat QC must be exhausted to a cold reservoir.” Max Planck Two of Kelvin’s & Planck’s joint statements of the 2nd Law of Thermodynamics 8. “It is impossible to extract an Lord Kelvin amount of heat QH from a hot reservoir and use it ALL to do work W. Some amount of heat QC must be exhausted to a cold reservoir.” 9. “It is impossible to design a cyclic device that takes heat from a reservoir and converts it to work Max Planck only (there must be waste heat) .” The nd 2 Law of Thermodynamics The Heat Flow Statement 10. “Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature. It never flows spontaneously in the reverse direction.” “A universe containing mathematical physicists will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures.” Sir Arthur Eddington’s (joke!) version of the 2nd Law of Thermodynamics! Definition: Heat Engine • A system that can convert some of the random molecular energy of heat flow into macroscopic mechanical energy. QH HEAT absorbed by a Heat Engine from a hot body -W WORK performed by a Heat Engine on its surroundings -QC HEAT emitted by a Heat Engine to a cold body The Second Law Applied to Heat Engines Efficiency (W/QH) = [(QH - QC)/QH] A “Heat Engine” That Violates nd the 2 Law (So it is Impossible!) Heat Reservoir Heat q Cyclic Machine Work Output=q Carnot’s Statements on the 2nd Law • These are essentially Corollaries of the Clausius & Kelvin-Planck versions of the 2nd Law: 11. It is IMPOSSIBLE to construct a heat engine that operates between 2 temperatures that has higher thermal efficiency than an ideal (reversible) heat engine. th,rev > th,irrev Carnot’s Statements on the 2nd Law • These are essentially Corollaries of the Clausius & Kelvin-Planck versions of the 2nd Law: 11. It is IMPOSSIBLE to construct a heat engine that operates between 2 temperatures that has higher thermal efficiency than an ideal (reversible) heat engine. th,rev > th,irrev 12. Reversible Engines (ideal or Carnot engines) operating between the same temperatures have the same th,rev The Carnot (Ideal, Reversible) Cycle (Carnot Engine) • This is assumed to be internally reversible. • Its interaction with the environment is reversible. Carnot Cycle Reversible Work: T Schematic: Qh Win Entropy S = constant Reversible Heat Transfer: Temperature T = constant Wout QL S Carnot Efficiency of a Heat Engine Definition: Heat Engine Efficiency Carnot Cycle Schematic W net,out QH QL QL th 1 QH QH QH QH Ql PS TH TL over a reversible cycle P QH Ql QH T H TH TL QL TL Carnot efficiency : S TH 0 QH W QL TL Carnot th,Carnot 1 Efficiency: TH TL This is the Maximum Efficiency possible for real engines! Definition: Refrigerator • A system that can do macroscopic work to extract heat from a cold body & exhaust it to a hot body, thus cooling the cold body further. Or, • A system that operates like a Heat Engine in reverse. QC HEAT extracted by a Refrigerator from a cold body W WORK performed by a Refrigerator on the surroundings -QH HEAT emitted by a Refrigerator to a hot body The nd 2 Law of Thermodynamics Clausius’ Statement for Refrigerators 13. “It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.” The nd 2 Law of Thermodynamics Clausius’ Statement for Refrigerators 13. “It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.” Or: There are no perfect Refrigerators! • This statement about refrigerators also applies to air conditioners & heat pumps which use the same principles. The Second Law Applied to Refrigerators Efficiency (QC/W) = [(QC)/(QH - QC)] Conceptual Example: You Can’t “Beat” the nd 2 Law of Thermodynamics • Question: Is it possible to cool your kitchen by leaving the refrigerator door open or cool your bedroom by putting a window air conditioner on the floor by the bed? Conceptual Example: You Can’t “Beat” the nd 2 Law of Thermodynamics • Question: Is it possible to cool your kitchen by leaving the refrigerator door open or cool your bedroom by putting a window air conditioner on the floor by the bed? (Hint: Recall the amusing video clip in which the teenage girl asks why air conditioners couldn’t be used to cool the outside!) Conceptual Example: You Can’t “Beat” the nd 2 Law of Thermodynamics • Question: Is it possible to cool your kitchen by leaving the refrigerator door open or cool your bedroom by putting a window air conditioner on the floor by the bed? (Hint: Recall the amusing video clip in which the teenage girl asks why air conditioners couldn’t be used to cool the outside!) • Answer: NO!!! Rather than cooling the kitchen, the open refrigerator will warm it up!! The air conditioner also will warm the bedroom. Entropy & The nd 2 Law: For a System in Equilibrium with a Heat Reservoir at Temperature T The 2nd Law of Themodynamics: • Heat flows from high temperature objects to low temperature objects because this process increases the system disorder. For a system interacting with a heat reservoir at temperature T & exchanging Heat Q with it, THE ENTROPY CHANGE IS: Q DS . T The 2nd Law of Thermodynamics can be used to generally classify Thermodynamic Processes into Three Types: 1. Natural Processes • These are Always Irreversible Processes. • These are also always Spontaneous Processes. 2. Impossible Processes • These violate either the 1st Law or the 2nd Law or both. 3. Reversible Processes • These are ideal processes & are never found in nature. • We’ll briefly discuss each with examples next. The Third Law of Thermodynamics “It is Impossible to Reach a Temperature of Absolute Zero.” On the Kelvin Temperature Scale, T=0K is often referred to as “Absolute Zero” Another Statement of rd The 3 Law of Thermodynamics: “The entropy of a true equilibrium state of a system at T = 0 K is zero.” • Strictly speaking, this statement is true ONLY if the quantum mechanical ground state is nondegenerate. If it is degenerate, the entropy at T = 0 K is a small constant & not 0! This version of the 3rd Law is Equivalent to: “It is impossible to reduce the temperature of a system to T = 0 K using a finite number of processes.” Now, two brief discussions of Philosophy!! (Religion?) 1. The 2nd Law & Life on Earth • Existence of low-entropy organisms like us has sometimes been used to suggest that we live in violation of the 2nd Law! • British cosmologist Sir Roger Penrose has considered this in his book “The Road to Reality: A Complete Guide to the Laws of the Universe” (2005). • In “The Road to Reality: a Complete Guide to the Laws of the Universe”, Penrose points out that “it is a common misconception to believe that the Sun’s energy is the main ingredient needed for our survival”. • He says, “What is important is that the energy source be far from thermal equilibrium”. • For example, a uniformly illuminated sky supplying the same amount of energy as the Sun, but at a much lower energy, would be useless to us. • Fortunately the Sun is a hot sphere in an otherwise cold sky. So, it is a low entropy source, which keeps our entropy low. The nd 2 Law & Life on Earth • Optical photons supplied by the Sun contain much more energy than the IR photons leaving us, since εph = hν. • Since the energy reaching us is contained in fewer photons, the Sun is a low entropy source. Plants utilize the low entropy energy, to reduce their entropy through photosynthesis. • We keep our entropy low by breathing oxygen produced by plants, and by eating plants, or animals ultimately dependent on plants. 2. The 2nd Law & the Arrow of Time! • One of the Deepest Philosophical Paradoxes of Modern Physics: Microscopic Physics is Time Reversal Symmetric. But, Nature is Not!! 2. The 2nd Law & the Arrow of Time! • One of the Deepest Philosophical Paradoxes of Modern Physics: Microscopic Physics is Time Reversal Symmetric. But, Nature is Not!! • The fundamental, Microscopic Theories of Physics (classical & quantum mechanical) don’t care which way time goes! • Newtonian Mechanics, Electromagnetism, Relativity, & Quantum Mechanics are all Time Reversal Symmetric. Arrow of Time: Why does time have a direction? (Always forward & never back!) • It’s NOT a feature of the microscopic laws of physics!! • Those work fine forwards or backwards in time; they are “Invariant under time reversal”! (t -t, pi -pi) • A common answer to why there is an arrow of time is: Entropy & The 2nd Law of Thermodynamics • It says that entropy S increases (in closed systems) with time. So The time derivative of the entropy must be positive: • That is: The 2nd Law says that entropy is NOT invariant under time reversal! Entropy & The 2nd Law of Thermo • This tells us that the entropy S must have the property that • So, The 2nd Law of Thermo is NOT invariant under time reversal! • Reconciling the 2nd Law of Thermodynamics, . (known to be correct) with the time reversal symmetry of the underlying microscopic physics is a Deep, Difficult, Philosophical Problem. • Starting from Boltzmann’s time until the present, many very smart people have tried to come up with a satisfactory explanation. So far, there is still no agreement among the experts on such an explanation. • To discuss this further would require at least an entire lecture! There is no time to cover it in class. Now, a brief (hopefully) humorous discussion L Some Popular (joke!) Versions of The Laws of Thermodynamics 1st Law: You can’t win. nd 2 Law: You can’t break even. 3rd Law: There’s no point in trying. Other Popular Versions of The Laws of Thermodynamics Version 1 Zeroth Law: First Law: Second Law: Third Law: You must play the game. You can't win the game. You can't break even in the game. You can't quit the game. Other Popular Versions of The Laws of Thermodynamics Version 1 Zeroth Law: First Law: Second Law: Third Law: You must play the game. You can't win the game. You can't break even in the game. You can't quit the game. Version 2 Zeroth Law: First Law: You must play the game. You can't win the game; You can only break even. Second Law: You can only break even at absolute zero. Third Law: You can't reach absolute zero! Version 3 Zeroth Law: You must play the game. First Law: You can't win the game. Second Law: You can't break even except on a very cold day. Third Law: It never gets that cold! Version 3 Zeroth Law: You must play the game. First Law: You can't win the game. Second Law: You can't break even except on a very cold day. Third Law: It never gets that cold! Version 4 Zeroth Law: First Law: Second Law: Third Law: There is a game. You can't win the game. You must lose the game. You can't quit the game. A joke!! “Murphy's Law” of Thermodynamics: “Things get worse under pressure!!” Murphy’s “Law”: “Anything that can go wrong, will go wrong!” . L Murphy’s “Law”: “Anything that can go wrong, will go wrong!” . L Mrs. Murphy’s “Corollary”: “Murphy was an optimist!” • There are many other variations of these kinds of “Laws”! • Whole books have been written compiling these kinds of “Laws” applied to various situations.