The Laws of Thermodynamics

The Zeroth Law of Thermodynamics “If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.”

Thermometers! This allows the design & the use of Thermometers!

The First Law of Thermodynamics Q = ∆Ē + W l F For Infinitesimal, Quasi-Static Processes đQ = dĒ + đW Both of these forms are expressions of the Conservation of Total Energy. So The Physical Meaning of the 1 st Law of Thermodynamics is that Total Energy is Conserved Heat absorbed by the system Work done by the system Change in the system’s internal energy

Rudolf Clausius (1850) The Physical Meaning of the 1 st Law of Thermodynamics  Conservation of Total Energy!!!! However, it says nothing about The Direction of Energy Transfer! Rudolf Clausius’ statement of the 1 st Law of Thermodynamics “Energy can neither be created nor destroyed. It can only be changed from one form to another.”

The 2 nd Law of Thermodynamics: “The entropy of an isolated system increases in any irreversible process & is unaltered in any reversible process.” This is sometimes called The Principle of Increasing Entropy  S  0 It gives the Preferred (natural) Direction of Energy Transfer It thus determines whether a process can occur or not. Change in the system entropy

Mathematically, this means that in any process ΔS ≥ 0 S → S max. or, at equilibrium, S → S max. 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 two cases are obvious examples of the Association of Entropy with Disorder. The 2 nd Law of Thermodynamics: “The entropy of an isolated system never decreases”. Change in Entropy

General Features 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, in 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 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.

2 nd Law of Thermodynamics: Various Statements of the 2 nd 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!

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.” 4.“During real physical processes, the entropy of an isolated system always increases. In the state of equilibrium the entropy attains its maximum value.” Three of Rudolf Clausius’ statements of the 2 nd Law of Thermodynamics

4.“It will arouse other changes while the heat from the single thermal source is taken out & is totally changed into work.” 5.“A process whose effect is the complete conversion of heat into work cannot occur.” Two of Lord Kelvin’s (William Thompson’s) statements of the 2 nd Law of Thermodynamics

6.“It is impossible to extract an amount of heat Q H from a hot reservoir and use it all to do work W. Some amount of heat Q C must be exhausted to a cold reservoir.” The Kelvin-Planck statement of the 2 nd Law of Thermodynamics Lord Kelvin Max Planck

7.“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 version of the 2 nd Law of Thermodynamics!

The 2 nd Law of Thermodynamics The Heat Flow Statement “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.”

Definition: Heat Engine  A system that can convert some of the random molecular energy of heat flow into macroscopic mechanical energy. Q H  HEAT absorbed by a Heat Engine from a hot body -W  WORK performed by a Heat Engine on the surroundings -Q C  HEAT emitted by a Heat Engine to a cold body

The Second Law Applied to Heat Engines Efficiency  (W/Q H ) = [(Q H - Q C )/Q H ]

A “Heat Engine” That Violates the Second Law

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. Q C  HEAT extracted by a Refrigerator from a cold body W  WORK performed by a Refrigerator on the surroundings -Q H  HEAT emitted by a Refrigerator to a hot body

The 2 nd Law of Thermodynamics Clausius’ Statement for Refrigerators “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  (Q C /W) = [(Q C )/(Q H - Q C )]

22 the 2 nd Law of Thermodynamics Conceptual Example: You Can’t “Beat” the 2 nd 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?

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? Answer: NO!!! Rather than cooling the kitchen, the open refrigerator will warm it up!! The air conditioner also will warm the bedroom. the 2 nd Law of Thermodynamics Conceptual Example: You Can’t “Beat” the 2 nd Law of Thermodynamics

Entropy & The 2 nd Law of Thermodynamics For a System in Equilibrium with a Heat Reservoir at Temperature T The 2 nd Law of Themodynamics: Heat flows from objects of high temperature to objects at low temperature because this process increases the disorder of the system. For a system interacting with a heat reservoir at temperature T & exchanging heat Q with it, the entropy change is:

The 2 nd 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 1 st Law or the 2 nd Law or both. 3. Reversible Processes –These are ideal processes & are never found in nature. We’ll discuss each with examples next.

Philosophy!!!! (or Religion?) The 2 nd Law & Life on Earth The existence of low-entropy organisms like ourselves Has sometimes been used to suggest that we live in violation of the 2 nd Law! Sir Roger Penrose has considered our situation in his work “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” (2005). Sir Roger 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 2 nd Law & Life on Earth The optical photons supplied by the Sun contain much more energy than the IR photons leaving us, since ε ph = hν. Since the energy 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.

Third Law The Third Law of Thermodynamics “It is Impossible to Reach a Temperature of Absolute Zero.” On the Kelvin Temperature Scale, T = 0 K is often referred to as “Absolute Zero”

Strictly speaking, this statement is true only if the quantum mechanical ground state is non- degenerate. If it is degenerate, the entropy at T = 0 K is a small constant, not 0! This version of the 3 rd Law is Equivalent to: “It is impossible to reduce the temperature of a system to T = 0 K using a finite number of processes.” Another Statement of The Third Law of Thermodynamics: “The entropy of a true equilibrium state of a system at T = 0 K is zero.”

The Laws Some Popular Versions of The Laws of Thermodynamics 1 st Law: 1 st Law: You can’t win. 2 nd Law: 2 nd Law: You can’t break even. 3 rd Law: 3 rd Law: There’s no point in trying.

Version 1 Zeroth Law:You must play the game. First Law: You can't win the game. Second Law: You can't break even in the game. Third Law:You can't quit the game. Version 2 Zeroth Law: You must play the game. First Law: 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. Other Popular Versions of The Laws of Thermodynamics

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: There is a game. First Law: You can't win the game. Second Law: You must lose the game. Third Law: You can't quit the game.

“Murphy's Law” of Thermodynamics: Things get worse under pressure!!