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.”

This allows the design & the use of Thermometers!

Q = ∆Ē + W đQ = dĒ + đW Total Energy is Conserved The First Law of Thermodynamics Q = ∆Ē + W For Infinitesimal, Quasi-Static Processes đQ = dĒ + đW Total Energy is Conserved Heat absorbed by the system Work done by the system Change in the system’s internal energy

Conservation of Total Energy!!!! The Direction of Energy Transfer! “Energy can neither be created nor destroyed. It can only be changed from one form to another.” Rudolf Clausius, 1850 The 1st Law of Thermodynamics is Conservation of Total Energy!!!! It says nothing about The Direction of Energy Transfer! (courtesy F. Remer)

The Second Law of Thermodynamics “The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process.” This is sometimes called The Principle of Increasing Entropy DS ³ 0 This gives the Preferred (natural) Direction of Energy Transfer This determines whether a process can occur or not. Change in entropy of the system (courtesy F. Remer)

Second Law of Thermodynamics Historical Comments Much 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 seem different than that just mentioned.

Various Statements of the Second Law “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! “It will arouse changes while the heat transfers from a low temperature object to a high temperature object.” Rudolf Clausius’ statement of the Second Law. Strange sounding?

Lord Kelvin’s (William Thompson’s) “It will arouse other changes while the heat from the single thermal source is taken out and is totally changed into work.” “It is impossible to extract an 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.” Lord Kelvin’s (William Thompson’s) statement of the Second Law. The Kelvin-Planck statement of the Second Law.

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 the surroundings -QC  HEAT emitted by Heat Engine to a cold body

The Second Law Applied to Heat Engines = (W/QH) = [(QH - QC)/QH] Efficiency = (W/QH) = [(QH - QC)/QH]

A “Heat Engine” That Violates the Second Law

Refrigerator  A system that can do macroscopic work to extract heat from a cold body and exhaust it to a hot body, thus cooling the cold body further. 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 2nd 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.” There are no perfect Refrigerators! This statement about refrigerators also applies to air conditioners and heat pumps which use the same principles.

The Second Law Applied to Refrigerators = (QC/W) = [(QC)/(QH - QC)] Efficiency = (QC/W) = [(QC)/(QH - QC)]

The 2nd Law of Thermodynamics can be used to classify Thermodynamic Processes into 3 Types: 1. Natural Processes (or Irreversible Processes, or Spontaneous Processes) 2. Impossible Processes 3. Reversible Processes We’ll discuss each more thoroughly with examples soon. (courtesy F. Remer)

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”

Another Statement of The Third Law of Thermodynamics “The entropy of a true equilibrium state of a system at T = 0 K is zero.” (Strictly speaking, this 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 is Equivalent to: “It is impossible to reduce the temperature of a system to T = 0 K using a finite number of processes.”

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

Other Popular Versions of The Laws of Thermodynamics 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.

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!!

From Statistical Arguments we’ve seen that a Quantitative Definition of Entropy is S  kBln() kB  Boltzmann’s constant  = (E)  Number of microstates at a given energy

Spontaneous Processes & Entropy Spontaneous Processes  Processes that can proceed with no outside intervention Entropy In qualitative terms, Entropy can be viewed as a measure of the randomness or disorder of the atoms & molecules in a system. 2nd Law of Thermodynamics Total Entropy always increases in a spontaneous process! So, Microscopic Disorder also increases in a spontaneous process!

Spontaneous Processes Processes that can proceed with no outside intervention. Example in the figure: Due to the 2nd Law of Thermodynamics the gas in container B will spontaneously effuse into container A. But, once the gas is in both containers, it will not spontaneously effuse back into container B.

The 2nd Law of Thermodynamics Processes that are spontaneous in one direction are not spontaneous in the reverse direction. Example in the figure: Due to the 2nd Law of Thermodynamics the shiny nail in the top figure will, over a long time, rust & eventually look as in the bottom figure. But, if the nail is rusty, it will not spontaneously become shiny again!!

For T > 0C ice will melt spontaneously. Processes that are spontaneous at one temperature may be non-spontaneous at other temperatures. Example in the figure: For T > 0C ice will melt spontaneously. For T < 0C, the reverse process is spontaneous.

Irreversible Processes Processes that cannot be undone by exactly reversing the process. All Spontaneous Processes are Irreversible. All Real processes are Irreversible.

Examples of Spontaneous, Irreversible Processes 1. Due to frictional effects, mechanical work changes into heat automatically. 2. Gas inflates toward vacuum. 3. Heat transfers from a high temperature object to a low temperature object. 4. Two solutions of different concentrations are put together and mixed uniformly. Note!! The 2nd Law of Thermodynamics says that the opposite processes of these cannot proceed automatically. In order to take a system back to it’s initial state, external work must be done on it.

Non-Spontaneous Process Spontaneous Processes (changes): Once the process begins, it proceeds automatically without the need to do work on the system. The opposite of every Spontaneous Process is a Non-Spontaneous Process that can only proceed if external work is done on the system.

Reversible Processes Reversible Process, In a Reversible Process, the system undergoes changes such that the system plus it’s surroundings can be put back in their original states by exactly reversing the process. changes proceed in infinitesimally small steps, so that the system is infinitesimally close to equilibrium at every step. This is obviously an idealization & can never happen in a real system!

Another Statement of the 2nd Law of Thermodynamics “The entropy of the universe does not change for Reversible Processes” and also: “The entropy of the universe increases for Spontaneous Processes” “You can’t break even”. For Reversible (ideal) Processes: For Irreversible (real, spontaneous) Processes:

Still Another Statement of the 2nd Law of Thermodynamics “In any spontaneous process, there is always an increase in the entropy of the universe.” The Total Entropy S of the Universe has the property that, for any process, ∆S ≥ 0.

More Examples of Spontaneous Processes Free Expansion of a Gas The container on the right is filled with gas. The container on the left is vacuum. The valve between them is closed. Now, imagine that the valve is opened. Valve Closed Vacuum Gas (courtesy F. Remer)

Free Expansion of a Gas The Entropy Increases!!!! After the valve is opened, for some time, it is no longer an equilibrium situation. The 2nd Law says the molecules on the right will flow to the left. After a sufficient time, a new equilibrium is reached & the molecules are uniformly distributed between the 2 containers. The Entropy Increases!!!! After some time, there is a new Equilibrium Valve Open Gas Gas (courtesy F. Remer)

Thermal Conduction A hot object (red) is brought into thermal contact with a colder object (blue). The 2nd Law says that heat đQ will flow from the hot object to the colder object. Hot Cold đQ (courtesy F. Remer)

After the 2 objects are brought into thermal contact, for some time, by the 2nd Law, heat đQ flows from the hot object to the colder object. During that time, it is no longer an equilibrium situation. After a sufficient time, a new equilibrium is reached & the 2 objects are at the same temperature. The Entropy Increases!!!! Warm After some time, there is a new Equilibrium (courtesy F. Remer)

Mechanical Energy to Internal Energy Conversion Consider a ball of mass m. It’s Mechanical Energy is defined as E = KE + PE. KE = Kinetic Energy, PE = Potential Energy. For conservative forces, E is conserved (a constant). Drop the ball from rest at a height h above the ground. Initially, E = PE = mgh Conservation of Mechanical Energy tells us that mgh = (½)mv2 h Just before hitting the ground, E = KE = (½)mv2 Mechanical Energy E is conserved! (courtesy F. Remer)

E = (½)mv2 = mgh KE = (½)mv2. KE' < KE. At the bottom of it’s fall, the ball collides with the ground & bounces upward. If it has an Elastic Collision with the ground, by definition, right after it has started up, its mechanical & kinetic energies would be the same as just before it hit: E = (½)mv2 = mgh In reality, the Collision will be Inelastic. So, the initial upward kinetic energy, KE', will be less than KE just before it hit. Just before hitting the ground, KE = (½)mv2. The collision is Inelastic, so right after it bounces, its kinetic energy is KE' < KE. Where did the lost KE go? It is converted to heat, which changes the internal energy Ē of the ball. As a result, the ball heats up!! (courtesy F. Remer)

So, the ball gets warmer!! dĒ = mcVdT The ball’s collision with the ground is inelastic, so it loses some kinetic energy: KE' < KE. The lost kinetic energy is converted to heat, which changes the ball’s internal energy Ē. So, the ball gets warmer!! In Ch. 4, we’ll show that, for an infinitesimal, quasi-static process in which an object heats up, changing its temperature by an amount dT, it’s internal energy change is dĒ = mcVdT m ≡ ball’s mass & cV ≡ specific heat at constant volume KE = (½)mv2 KE' < KE The change in the ball’s internal energy is dĒ = mcVdT (courtesy F. Remer)

The Ball’s Entropy Increases!!!! Multiple Bounces of the ball  Multiple Inelastic Collisions with the ground. When it finally comes to rest after several bounces, it may be MUCH warmer than when it was dropped! The ball loses more KE on each bounce & it eventually stops on the ground. Thus, after sufficient time, it tends towards Equilibrium The more bounces the ball has, the warmer it gets! The Ball’s Entropy Increases!!!! (courtesy F. Remer)

“Impossible Processes”  allowed by the 1st Law of Thermodynamics Brief Discussion of “Impossible Processes”  Processes which are allowed by the 1st Law of Thermodynamics but which Cannot Occur Naturally because they would violate the 2nd Law of Thermodynamics. Any process which would take a system from an equilibrium state to a non-equilibrium state without work being done on the system would violate the 2nd Law of Thermodynamics & thus would be an Impossible Process! (courtesy F. Remer)

Examples of Impossible Processes Example 1: “Free Compression” of a Gas! Initially, the valve is open & gas molecules are uniformly distributed in the 2 containers. Valve Open Gas Gas After some time, all gas molecules are gathered in the right container & the left container is empty. The Entropy Decreases!! Gas Vacuum Valve Open (courtesy F. Remer)

Initially, an object is warm. Thermal Conduction Initially, an object is warm. Warm After some time, the left side is hot & the right side is cold . Hot Cold The Entropy Decreases!! (courtesy F. Remer)

Conversion of Internal Energy to Mechanical Energy Initially, a ball is on the ground & is hot. Hot Warm After some time, the ball begins to move upward with kinetic energy KE = (½) mv2 & it cools down! The Entropy Decreases!! (courtesy F. Remer)

Cannot occur without the input of work Impossible Processes Cannot occur without the input of work đW (courtesy F. Remer)

In such a process, the System’s Entropy Decreases, but the Total Entropy of the System + Environment Increases Decrease in Entropy Environment đW Increase in Entropy (courtesy F. Remer)