Don't Panic

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# Thermodynamics

The word thermodynamics was coined by none other than James Joule (1818--1889).

Thermodynamics, which physicists (in particular physics students) abbreviate to thermo, can be briefly described as the science of heat energy (properly called internal energy) and temperature.

But a real definition must be a bit longer:

Thermodynamics is the science of the thermodynamic state of systems. This state is characterized or defined or determined by thermodynamic variables which include heat energy (properly called internal energy), temperature, pressure, volume, density, mass, entropy, phase, and many others too. These variables are functions of the thermodynamic state and are called state functions: they are independent of the history that resulted in the thermodynamics state. Energy transformations, most importantly heat flow and macroscopic work done, are part of thermodynamics. Thermodynamics encompasses both thermodynamic equilibrium and non-equilibrium states. In modern version of thermodynamics, the average microscopic state of the system and how it determines the macroscopic variables mentioned above is included.

Of course, we have to define some of the terms in the definition---we'll do that mostly in following sections.

Some of the terms are familiar, but not, in some cases, their science definitions.

An obvious first thing to define is system.

A system is any set of objects, you wish to study.

Everything else in the universe is the environment or surroundings.

Caption: "The boundary between a system and its surroundings".

Credit: User: Wavesmikey.

Public domain.

Division of the universe into system and environment is useful in analyzing the behavior of both.

Often one models both by simplified versions.

The real system and environment being too complex to understand and a only a certain level understanding may not be required.

Often one idealizes both system and environment. This means one replaces real components by ideal versions.

Often modeling and idealization allow one to use basic principles to predict to the system and environment behavior with some degree of approximation.

``To idealize'' means discounting complicating factors.

Because the system is the main object of interest, the environment need only be studied or modeled insofar as it affects the system.

Thermodynamics has 4 basic laws in the usual formulation---but people often talk of the three laws of thermodynamics because one law is called the zeroth law.

The laws are analogous to Newton's three laws of motion in Newtonian physics in some respects.

But actually, just as in Newtonian physics, there must be other laws too.

The laws of thermodynamics usually along with many other laws allow you to predict the future of a system provided the initial conditions and environment are specified.

Oddly enough, they do NOT allow you to necessarily predict the past of a system in principle.

This is unlike the case of purely macroscopic, non-thermodynamic system governed by Newtonian physics, classical electromagnetism.

By a purely macroscopic, non-thermodynamic system, we mean one where there is no heat flows and there purely thermodynamic quantities, like temperature, play no role.

Newtonian physics, classical electromagnetism plust intial conditions (positions and velocities) and a fully specified environment for all times would allow you to predict the system to both the past and the future.

The situation is completely determined.

But in thermodynamics, once a thermodynamic equilibrium for a thermodynamic system, its past is erased.

How it got that thermodynamic equilibrium is not encoded in the thermodynamic variables (i.e., the state functions).

You might know its past from other outside sources of information, but not from the system itself.

Note that in both our non-thermodynamic system and thermodynamic system examples, we have not discussed the microscopic realm.

We can do that as a philosophical digression.

First note that classical physics includes Newtonian physics, classical electromagnetism, and classical classical thermodynamics (i.e., thermodynamics without reference to the microscopic realm).

Now imagine the classical physics was exactly true---which is NOT the case for reasons that we discuss below.

Imagine there was an omniscient perfect calculator.

If he/she were given all the positions and velocities of all particles in the world at one instant in time, then using classical physics (but only needing Newtonian physics and classical electromagnetism), he/she could calculate all past and future at once.

Classical classical thermodynamics would be superfluous to this calculation since all macroscopic behavior should be determined from microscopic behavior.

The calculation can be done in principle in a world in which classical physics was exactly true.

This is because classical physics is completely deterministic.

We use statistical methods all the time in classical physics, but this is because we lack some information or don't want to bother with it.

For example in throwing

Then, Newtonian physics, classical electromagnetism The situation depends on which set of principles one adopts.

Consider a system whose environment is specified for all times.

In classical physics (which includes Newtonian physics, classical classical thermodynamics, and classical electromagnetism), if one knows the present exactly right down to the location and velocity of every classical particle and all physical fields (i.e., the electromagnetic field and gravitational field), all the past and all the future of the system could be predicted by a omniscient perfect calculator in principle.

In classical thermodynamics (which does not consider the microscopic realm and treats it as unknown), the future of the system can be predicted exactly from all present macroscopic variables---by our friend the omniscient perfect calculator---but the past of the system can't be.

As we will see the macroscopic past of system is erased for a system that has reached thermodynamic equilibrium.

Caption: "The Last of the Spirits, from Charles Dickens: A Christmas Carol.".

Credit: John Leech (1817--1864).

Linked source: Wikipedia image . http://en.wikipedia.org/wiki/Image:The_Last_of_the_Spirits-John_Leech,_1843.jpg.

Public domain.

Which perspective is correct?

That of classical physics or that of classical thermodynamics?

Well in a true classical world, the former is and all past and future are predictable.

If one limits oneself to classical thermodynamics the past isn't necessarily predictable.

The above statements take an enormous qualification because of quantum mechanics.

Caption: "The wave function of a particle in an infinite 2D well for nx = 4 and ny = 4." (2008).

The x-y plane is the spatial region of the well (or 2-d box).

In quantum mechanics, the the wave function Psi of a system tells you everything you can know in principle about the system.

In this case, there is a particle in a 2-dimensional box with impenetrable walls.

The particle exists in a superposition of positions: it's everywhere at once in the box, but only in part.

Where the wave function is zero, the probability of finding the particle there is zero.

The probability increases as the square of the wave function: i.e., Psi**2

Psi**2 dxdy is the probability of finding the particle in dxdy on a measurement.

Quantum mechanics is a probabilistic theory.

In many cases, all one can predict is the probabilities for events.

This is intrinsic.

In quantum mechanics, the world is fundamentally probabilistic, not deterministic.

Credit: User:Keenan Pepper.

Permission: Public domain at least in USA.

In the standard interpretation of quantum mechanics---which may be wrong---a system is NOT in a single definite state, but is in a superposition of states.

If you knew the universal wave function, you would know everything about the present that you could know, but you couldn't even in principle predict the whole future even if you were the omniscient perfect calculator.

This is because the universe is intrinsically probabilistic, not deterministic, in quantum mechanics.

I think whole past can't be predicted either, but I'm not sure of the argument.

So in quantum mechanics with the standard interpretation (which means in reality if the standard interpretation is correct), the microscopic future cannot be exactly predicted even in principle.

But who cares what various atoms are doing if the macroscopic future can be predicted in principle.

If the microscopic future cannot be exactly predicted, the macroscopic future cannot be predicted either.

There are pathways for microscopic randomness to be amplified to the macroscopic realm.

My favorite, example, is the guy with a geiger counter.

He's counting the decays of some radioactive material.

Radioactive decay is intrinsically statistical (in the standard interpretation).

The average count rate is constant, but the count in any time period will fluctuate randomly from average count rate.

The guy bets himself he will get a coffee if he counts the mean rate or more for 10 seconds and not if not.

All of the future history of humanity is now determined by an intrinsically random process.

But it's not just guys with geiger counters making bets with themselves.

There are many other applification processes probably even in our thought processes.

So if the standard interpretation of quantum mechanics is correct, life really is a gamble.

All of this is philosophical.

But it's important anyway since one would like to know the truth.

Caption: "Truth (1896). Olin Warner (completed by Herbert Adams). Left bronze door at main entrance of the Library of Congress Thomas Jefferson Building.".

The mirror I get. The snake must be a symbolic serpent.

Maybe antitruth.

In any case, "The Truth Is Out There" as they used to say on The X-files.

Credit: ``Artist is Olin Levi Warner (1844--1896). Photographed in 2007 by Carol Highsmith (1946--), who explicitly placed the photograph in the public domain.''

Linked source: Wikipedia image . http://en.wikipedia.org/wiki/Image:Truth-Warner-Highsmith.jpeg.

Public domain.

A few more prefatory remarks can be made---this means I started digressing at random and never cleaned up the discussion.

Classical thermodynamics avoids anything consideration of the microscopic constituents of matter and radiations: i.e., atoms, molecules, photons, etc.

This purely classical approach is not much done nowadays.

We do understand thermodynamics in terms of microscopic constituents and it makes sense to discuss them as we discuss thermodynamics---even if we in this lecture can't rigorously prove things from microscopic arguments.

It seems incredibly pedantic and obscurantist not to do so.

Thermodynamics is divided into two branches: equilibrium thermodynamics (TE) and non-equilibrium thermodynamics (NTE).

The former deals with time-independent systems or those that vary slowly enough in time that they can be treated as time-independent at any instant and the latter with systems which maybe time-dependent or in time-independent steady-state---like a lake with inflow and outflow, they are unchanging, but not isolated.

There is no absolute separation between the two branches.

One often includes effects of non-equilibrium thermodynamics in studies of equilibrium thermodynamics at least in some non-detailed or approximate way.

One does have to have some way of getting TE state to another even when one is trying to stick to TE as much as possible.

Full NTE is immensely harder than TE, and so we skirt it in elementary discussions like this one.

``Skirt'' doesn't mean avoid entirely, but just not to plumb the depths.

Chemistry certainly comes into thermodynamics and chemical laws become auxiliary laws whenever chemical changes happen during thermodynamic changes.

But we skirt chemistry in elementary discussions like this one.

Macroscopic motions and changes are NOT directly part of thermodynamics, but they can be involved in during thermodynamic changes.

Thermodynamic changes of a system can do macroscopic work of either positive or negative sign.

This work is usually done by pressure.

Of course, such work is all important to the practical application of thermodynamics in understanding, e.g., heat engines.

We discuss heat engines in lecture Heat Engines, Refrigerators, and the Carnot Heat Engine.

Two examples of heat engines are the internal combustion engine (which is used to power, e.g., automobiles) and the steam turbine (which is used to generate, e.g., electric power).

# Thermodynamic Variables

Thermodynamic variables are those things that characterize the STATE of system.

The macroscopic motion of the system is usually excluded from the thermodynamic state description.

The macroscopic motion can be isolated from the thermodynamics state especially in general discussion.

But the two can be connected through the macroscopic work done by or on a system.

We will NOT exhaustively discuss the thermodynamic variables.

There are relationships among them dictated by laws of thermodynamics and other principles too. We mostly skirt these.

There are two main categories: extensive variables and intensive variables.

EXTENSIVE VARIABLES are those that scale with the system: e.g.,

If you scale the system up by a factor f, all the EXTENSIVE VARIABLES scale up by f.

INTENSIVE VARIABLES do not scale with the system.

Typically they are ratios of EXTENSIVE VARIABLES--- since each EXTENSIVE VARIABLES variable in the ratio scales with the system, the ratio is unchanged since the scaling factor cancels out. Examples are:

Density which is the ratio of mass over volume.

Specific internal energy which is internal energy per unit mass or per unit volume.

Temperature which is the average energy of a microscopic particle per degree of freedom. The definition requires some qualification and discussion which we give in section Temperature.

But one can also say that a href="http://en.wikipedia.org/wiki/Temperature">Temperature is a measure of mean microscopic kinetic energy.

Pressure which is the magnitude of force per unit area exerted by a system at any point inside the system and on its boundaries.

Pressure is usually isotropic. A pressure sensitive surface in any orientation at a point in a system reads the same value.

Of course, you may have account for macroscopic flows in the systm.

There are laws and formulae relating the thermodynamic variables, and so only a subset are needed to specify a thermodynamic state.

There is no fixed subset.

For a thermodynamic equilibrium system for example, one could specify fully specify a system using temperature, density, composition (i.e., the relative abundances of all the elements), and mass---I think.

Caption: "Isotherms of an ideal gas in pressure (p) vs. Volume (V): hyperbolas".

The ideal gas law is the simplest of all laws relating thermodynamic variables:

```                        PV=nRT  ,

where for a system of
ideal gas

P is pressure,
V is volume,
n is the number of moles
R is the universal gas constant
and
T is temperature
on the Kelvin temperature scale.

```

If temperature is fixed, then pressure is decreases with volume as the plot shows.

Isotherms are curves of constant temperature.

Real gases approach ideal gas in the limit of low density.

The ideal gas law is often an excellent approximation to real gases.

Credit: Geoff Martin

Public domain.

# Internal Energy

Internal energy is the sum of all microscopic forms of energy of a system.

It's actually hard to define microscopic forms of energy intelligibly in a few sentences.

They are NOT the kinetic energy of average motion of the system and NOT the potential energy of the system.

They are the uncorrelated kinetic energies of the particles (e.g., atoms, molecules, and electrons) making up the system and the potential energies of the particles relative to each other (which in the case of bonded atoms, molecules, and electrons are the chemical bonding potential energies).

The microscopic forms of energy include the energy of thermal radiation that is somehow confined to the system: e.g., the thermal radiation trapped in the interior of the Sun which is thermodynamic equilibrium with the matter---we discuss thermodynamic equilibrium below in the secion Thermodynamic Equilibrium.

The key energy form for understanding is kinetic energy of the microscopic motions of particles.

If that kinetic energy were removed all removed (which actually can't happen as we discuss in section Temperature), then the system would be thermodynamically inert left to itself.

The motions can be consider random in the sense that they are uncorrelated with each other, so cannot sum up to a macroscopic motion. They do have distributions of behaviors: e.g., a distribution of velocities.

This is actually somewhat definitional. If some motions do sum up to a macroscopic motion, they are not microscopic motion.

For example, consider a macroscopic flow of a fluid. The individual particles that make up the fluid have two components to their motion. Random motion and a flow motion: the former is microscopic and the latter macroscopic.

Let's digress---because I did digress--on motions in matter.

In the case of gases, the microscopic motions are those of free-flying particles that move in all directions isotropically and undergo random collisions.

Most of the time atoms and/or molecules in a gas are not touching in the sense that regions of strong interaction are not touching. In fact, usually there is a lot of empty space between the atoms and molecules in ordinary gases in the terrestrial environment.

In the case of liquids, the particles are loosely bonded to each other. They are touching in the sense that their regions of strong interaction are in contact. They stay in contact, but slide over each other. Their microscopic motions are random (i.e., uncorrelated with each other).

Solids are a bit different.

In many, but not all, cases, the mean position of the particles in a solid is ordered.

The atoms and/or molecules in an ordered pattern called a lattice.

Such solids are crystals

Usually, crystalline ordering doesn't extend very far.

Macroscopic samples of solids are typically made up of crystallites (also called grains) that have crystalline order, but the crystallites are randomly ordered.

The crystallites are fused together to make the solid solid.

On the other hand, Amorphous solids have no long-range order: e.g., common window glass whose main component is silica (SiO2).

In solids atoms and/or molecules are fixed in some position which if they are crystalline will be on a lattice

But they have random vibrations from their exact mean positions.

Microscopic energies are those relevant to the behavior of molecules, atoms, thermal radiation, and the microscopic electromagnetic fields.

Energies of the atomic nucleus usually can be neglected in terrestrial and many other environments.

The nuclei are mostly all in their lowest energy state (the ground state), and so are thermodynamically inert internally.

In some astrophysical environments, like supernovae in their explosion phase, the nuclei can become thermodynamically active.

Radioactive decay of unstable nuclei can create internal energy above the ground state, but that's a story for another day.

The most obvious of these microscopic energies is the translational kinetic energy of atoms and molecules in gases.

Frequently, for simplicity people speak as if the random kinetic energies were the only kind of internal energy.

But this is really wrong.

Almost all other forms of energy can have microscopic forms: e.g., potential energy thermal radiation, and perhaps other forms depending on how one thinks of things.

A bit of terminology clarification is needed.

1. Internal energy is often used a synonym for thermal energy, but it's actually not exactly a synonym. I don't want to get into the fine distinction, and so I'll avoid the term thermal energy.

2. In actual speach heat energy or heat is used as a synonym for internal energy.

It's not accepted as formally correct, and so I avoid writing heat energy usually, but I don't avoid saying it.

3. In formal physics jargon, heat is a transferred amount of internal energy or internal energy in transit.

But in the author's opinion, this concept of heat is redundant.

One can just say transferred internal energy.

In which case, ``heat'' can be used the way people (including physicists) tend to use it: as a synonym for internal energy.

I avoid using heat as a synonym for internal energy in writing, but in speech it keeps slipping out as a synonym.

As far as I can tell everyone does use it as a synonym for internal energy when speaking loosely.

# Temperature

What we read off a thermometer---or what we sense with our body.

But what we read off an ordinary alcohol thermometer is the volume of red-dye-colored ethanol (Sci-Tech Dictionary: alcohol thermometer) and what we sense with our body is somewhat qualitative and ill-defined.

In physical theory, temperature is the average energy per degree of freedom of a particle (e.g., atom, molecule, photon which is the ``particle'' of light).

For example, the three orthogonal directions of space are the three translational degrees of freedom.

Particles also have rotational, vibrational, potential energy, and internal degrees of freedom.

We will not go into details.

But it's useful to think of temperature as a measure of the mean kinetic energy per particle.

The precisely defined physical temperature can be correlated to observables that approximately measure it over some range of temperature.

An observable calibrated to read temperature is the volume of ethanol in an alcohol thermometer.

This can be done since volume increases with temperature usually for most materials and ethanol is conveniently calibratable.

Many other such observables exist: e.g., a thermocouple which uses an electrical potential difference to measure temperature.

There is a coldest.

This is the absolute zero of temperature.

Caption: "The Endurance at night during Ernest Shackleton's Imperial Trans-Antarctic Expedition in 1914."

Cold, but absolute zero is colder.

Light bulbs were used to illuminate the ship during the long antarctic night.

The ship was trapped in the ice and would break up---the whole crew was rescued.

See Roger Ebert's review of the film South made during the Shackleton expedition.

Cold, but absolute zero is colder.

Credit: F. A. Worsley and Scott Polar Research Institute.

Linked source: Wikipedia image . http://en.wikipedia.org/wiki/Image:Shackleton_expedition.jpg.

Public domain.

At absolute zero all kinetic energy that can be removed from a system has been removed.

The particles are all in their lowest energy state, but there is an irremovable kinetic energy for each particle or vacuum energy for radiation.

This irremovable energy is the zero-point energy.

In classical physics there is no zero-point energy.

So, for example, in a classical physics the molecules of a gas at absolute zero (with condensation and gravity magically turned off) would just come to rest in space.

So nature has given us an absolute zero of temperature: a coldest that can be.

Nature has not, however, given us a standard unit of temperature: i.e., a unit that has significance for systems in general.

But liquid water is all-important for life (including us).

Our bodies are mostly water: on average 55 % for men and 51 % for women (Wikipedia: Body Water).

Water is the universal solvent and medium for transport of materials (chemicals, cells) in living bodies. We don't know how these things would go on without liquid water.

As the saying goes: ``you can take the buoy out of the ocean, but you can't take the ocean out of the boy.''

Given this fundamental importance for life, the Celsius temperature scale which divides the temperature difference between melting of ice and boiling of water into 100 units (which the are in modern terminology the Celsius degrees) makes sense.

Caption: ": Part of an oil painting of Anders Celsius. Painting by Olof Arenius (1701 - 1766). The original painting is placed in the astronomical observatory of Uppsala University."

Anders Celsius (1701--1744) was a Swedish astronomer who proposed the first version of the Celsius scale.

Credit: Olof Arenius (1701--1766).

Public domain.

The exact modern definition of the Celsius degree is not based on that old prescription. But the modern definition is very close to the old prescription and the degree Celsius retains its orginial significance.

Of course, the zero-point of the Celsius scale is the melting temperature of water nearly.

The temperature scale with its zero-point at absolute zero is the Kelvin temperature scale or thermodynamic temperature scale or absolute temperature scale.

The Kelvin temperature scale degree is the kelvin (K) which is set equal to the Celsius degree.

That makes conversion between the Kelvin scale and Celsius scale simple.

Absolute zero is -273.15 Celsius degrees exactly.

Thus,

```
T_K = T_C + 273.15

T_C = T_K - 273.15

```
There is not much point in the learning the conversions to Fahrenheit scale which is obsolete for science and technology and---in yours truly's view---ought to be phased out altogether.

The United States is the only major country to use it. A few other minor countries like Belize use it too---where the heck is Belize?

In fact, there's not much point to the Celsius scale either---in yours truly's view.

We could just give temperatures on the Kelvin scale for everything. We would just say 2 something or 3 something for everyday temperatures.

But no one ever listens to me.

```
---------------------------------------------------------------------

Short Table of Temperature Scale Comparisons

---------------------------------------------------------------------
Event                 Kelvin         Celsius       Fahrenheit
(K)             (C)            (F)
---------------------------------------------------------------------

absolute zero            0           -273.15          -459.67

melting point of ice   273.15           0                32

moderate chill         290.00          16.85             62.33

moderate warmth        300.00          26.85             80.33

boiling point of water 373.15         100               212

---------------------------------------------------------------------

The melting and boiling point numbers are representative since exact
values depend on the specification of pressure.

---------------------------------------------------------------------

```

# Thermodynamic Equilibrium

Thermodynamic equilibrium is the state of a SYSTEM when no thermodynamic changes are occurring.

All the thermodynamic variables are staying constant in time.

The temperature is constant throughout the SYSTEM.

We won't attempt any proof of this statement.

Microscopic changes are happening to the SYSTEM, but at the macroscopic level it is unchanging.

Thermodynamic equilibrium is a timeless state.

Thermodynamic equilibrium is also a dead state.

Nothing can live in thermodynamic equilibrium.

So thermodynamic equilibrium is rather boring.

But it is easy to analyze compared to non-equilibrium states.

And, in fact, we can analyze non-equilibrium states using equilibrium thermodynamics accepting that there are certain approximations.

In some cases, those approximations are very small, but in some they are not.

One can often consider the system as passing through a sequence of thermodynamic equilibrium states.

Such processes are called quasistatic process since they must be sufficiently slow, but often that is not very slow.

Even if the QUASTATIC APPROXIMATION is not very good, it might be useful for crude or order-of-magnitude calculations.

Question: Is the observable universe in thermodynamic equilibrium?

The Hubble Deep Field.

This is about 1/4 of the original HST deep field image (1995dec18--28): a random empty speck of sky: size here is about 1/60 of a degree: the whole deep field was 2.7 X 2.7 arcminutes.

It is true color (as much as possible) and the blue galaxies must be very blue to still be blue after high redshifts???. There are hundreds of galaxies visible: some the vary faintest are as they were probably only a billion years after the Big Bang. Most may be from 6--9 billion light years or 6--9 billion years in look-back time.

Credit: NASA/HST. This image is the public domain as it was created by and is not otherwise noted as copyrighted.

Now that you've looked at a fair fraction of it.

1. Yes.
2. No.
3. Maybe.

Profoundly not.

Stars are hot and space is cold (in the sense that the main component of electromagnetic radiation (EMR) in space has a temperature of 2.725 K) and there is a constant flow of internal energy in the form of electromagnetic radiation from the stars into space.

In our current understanding, the stars will never succeed in heating up the observable universe: it will cool forever.

But our current understanding may not be forever.

# The Zeroth Law of Thermodynamics

Actually, systems are in thermodynamic equilibrium if they have the same temperature as measured by some theoretically defined thermometer.

Most elementary textbooks blandly say that the zeroth law allows one to define a temperature scale---without bother to specify how exactly.

The Wikipedia article on the zeroth law informs me that this consequence of the zeroth law is actually debatable.

But the zeroth law is certainly necessary if not sufficient for setting up a temperature scale.

The Wikipedia article on the zeroth law also informs the zeroth law is necessary to complete thermodynamics---but the argument is beyond our scope and my patience at the moment.

# The First Law of Thermodynamics

1st law of thermodynamics in a specialized version often seen in textbooks is

```
(Delta E) = Q - W   .

(Delta E) is change in the
internal energy
of a
system.

Q is heat
used in its proper sense of flow of
internal energy.
It is is positive for inflow and negative for outflow.

W is work done
by the
system.
This is macroscopic
work
that can be used, for example, to push pistons in the cylinders
of a heat engine.
It is is positive for outflow and negative for inflow.

As a formula W is given by

W = F * (Delta d) = P * A * (Delta d) = P * (Delta V)   .

F is the force of
pressure.
(Delta d) is the distance the volume of the
system expands/contracts.
A is the area over whihc the pressure
acts.
(Delta V) is the change in volue of the
system.

The negative sign in front of work W is a bit of a nuisance, but we like to think of
pressure as a positive quantity
and an increase in volume
as a positive change, and so we are stuck with an explicit negative sign.

```
In physics jargon, work done by a thermodynamic system is called PdV work where ``d'' is like Delta, but more calculusy.

But PdV work can also be called pressure work.

1st law of thermodynamics is essentially the law of conservation of energy in the context of thermodynamics.

Besides telling you that energy is conserved, it also tells that internal energy can be converted into macroscopic energy via work and vice versa.

Among other things, then 1st law of thermodynamics is part of the theoretical underpinning for heat engines and refrigerators.

There are, however, restrictions on the conversion process not given by 1st law of thermodynamics.

The 2nd law of thermodynamics and 3rd law of thermodynamics give those restrictions.

Note that the 1st law of thermodynamics implies non-equilibrium thermodynamics in principle since it is about change.

But the details of non-equilibrium thermodynamics can in many, but not all, calculations be skipped.

As mentioned above in section Thermodynamic Equilibrium, one can often consider the system as passing through a sequence of thermodynamic equilibrium states in a quasistatic process.

# Pressure

Pressure is what does work in the context of thermodynamics: that is PdV WORK (Section The First Law of Thermodynamics).

Pressure is an isotropic force magnitude per unit area on any planar slice through matter for matter at rest.

Pressure is regarded as a scalar since the pressure force is isotropic: i.e., pushes equally in all directions at any one point in space.

Gases have and liquids have pressure always.

Gases tend to expand indefinitely under zero pressure.

Liquids generally evaporate if the pressure: i.e., the liquid phase ceases to exist in thermodynamic equilibrium conditions.

In flowing fluids (which includes liquids and gases) there is anisotropic transport of momentum (which amounts to a force) and so in a sense ``anisotropic pressure'' but that term seems to be avoided.

Solids compress when subject to pressure and then have internal pressure.

But under vacuum conditions, they have zero pressure and are often only slightly decompressed from their state under room pressure.

In gases it is caused by the collisions of the molecules

A schematic movie of a confined gas.

The molecules have kinetic energy which can be measured by temperature.

The microscopic collisions of the molecules give rise to macroscopic pressure which is a force per unit area on any planar slice through the gas.

Credit: Greg L. According to Wikipedia permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version.

About how many molecules are there in a small sample of air?

Air is mostly Ni_2 (i.e., diatomic nitrogen) (Wikipedia: Atmospheric chemistry.

75.3 % by mass and 78.082 % by volume in dry air (Wikipedia: Nitrogen).

The way things have been made to work out in chemistry/physics, 28 grams of Ni_2 has about 6.022*10**23 molecules = 1 mole.

So a lot of molecules go up into making a little bit of gas.

So there are usually lots of tiny collisions in general to give pressure at macroscopic level.

Thus there seems to be a continuum of pressure push.

Remember, small molecules are tiny: of order 1 or a few Angstroms.

Recall 1 Angstrom = 0.1 nanometers = 10**(-10) m.

Note air density at sea level is about 1.2 kg/m**3.

```              (1000 g)/(28 g/mole) = approximately 30 moles

of N_2 in a cubic meter of air
```

Pressure always gives a repulsive force, in fact.

There may be a cosmological negative pressure caused by dark energy which is gives a univeral tension which cancels out completely and oddly enough gives acceleration to the universal expansion---but let's not get into that estoric subject.

But there are contexts where it looks attractive.

For example, suction cups.

When fluids are in motion, pressure combined with momentum transport can have striking effects---which we won't worry about too much---except we will look at aerodynamic lift for a moment for fun and profit.

Aerodynamic lift is that special arrangement of pressure and momentum transport in fluids that, among other things, lets airplanes fly.

Nothing else is holding them up---gravity pulls them down---they are sitting on air.

Consider the first powered flight.

The first powered flight of the Wright flyer on 1903 December 17.

Orville Wright flew for 36.5 meters at 6.8 mi/h for 12 seconds.

He's in superman position.

Wilbur Wright must be the observer.

He didn't fly very high: altitude about 10 feet; the Wright brothers were not daredevils.

They had no desire to repeat the Icarus story.

The location is sand dunes called Kill Devil Hills, 4 miles south of Kitty Hawk, North Carolina.

The picture was taken by John T. Daniels of Kill Devil Hills Life Saving Station using Orville Wright's tripod.

Credit: John T. Daniels, 1903 December 17. Created before 1923, and so the public domain at least in the U.S. No copyright is claimed for any modification.

There are actually two components to aerodynamic lift: reaction lift and Bernoulli lift.

We can demonstrate both reaction lift and Bernoulli lift and how we fly with an elaborate apparatus.

Blow below a sheet of paper and the paper rises: this is reaction lift.

This understood in terms of Newton's 3rd law: for every force there is an equal and opposite force.

The paper forces the flowing air down: the flowing air exerts an opposite force pusing the paper up.

The reaction force of the air on the paper is due to the macroscopic flow in a direct sense.

But that flow couldn't exert a force without air pressure.

More mysteriously, blow above the paper and the paper rises again: this Bernoulli lift.

It turns out that making the air move fast through one's pursed lips lowers its isotropic pressure.

The air above the paper, then has lower pressure than air below.

The result is a lift force.

Airplanes obtain Bernoulli lift through the shape of their wings which force faster flow above than below the wing.

Both reaction lift and Bernoulli lift are important for powered flight.

The reaction lift provides most of the lift in fact, but it's unstable and relying on reaction lift alone would cause a lot of bouncing around.

The Bernoulli lift provides a stabilizing force.

15 psi is the whole weight of a 1 square inch column of air up to space.

It is a lot of force.

How do our bodies stand it?

Solids and liquids do NOT compress or decompress much under that pressure.

And the gas pressure inside is much the same as outside.

Even in vacuum, our bodies can hold our internal air pressure in.

We don't blow up in a vacuum---but we'd soon die from the bends (decompression sickness) and asphyxia and our eardrums might burst.

The author likes psi if though they have that ``p'' in front.

``Trouble, oh we got trouble,
Right here in River City!
With a capital "T"
That rhymes with "P"
And that stands for ...''

``Calls himself Hill, Professor Harold Hill ...''

A man with whom I've a lot of sympathy---he knows nothing about music.

So psi is not SI.

But psi does have a convenient size for human purposes.

Question: Approximately what is ordinary tire pressure in psi?

1. 1 psi.
2. 15 psi.
3. 30 psi.
4. All of the above.

The manufacturer gives precise specifications for optimum performance.

Pneumatic tires are used for their bouncingness---i.e., to absorb shocks, etc.

The SI unit of pressure---the pascal (Pa) is rather tiny for human purposes.

```
It is, of course, 1 N per m**2

Remember 1 N = 0.2248 lb = approximately 1/5 of pound.

Spread 1 N over a square meter, and that's not much pressure.

It's 1.4504*10**(-4) psi.

```
Ordinary air pressure in pascals is about 10**5 Pa = 0.1 MPa.

So we could get used to megapascals.

Of course, for scientific and most engineering uses SI units are preferred for the standard reference units though not always the units of convenience.

# Entropy

Entropy in physics is a quantitative thermodynamic variable like temperature and pressure---but more arcane.

There are formulae to give its value---but we won't give them.

Rudolf Clausius (1822--1888), the discoverer of the entropy concept.

Actually, in most 19th century photos, people look grim and/or blank.

The photos were often long-exposures lasting minutes, and the subjects had to hold their faces in relaxed expression. Their heads were often rested on headrests (hidden at the back) to keep the heads from moving.

Clausius looks too fierce for a long-exposure. Maybe the just always looked that way when relaxed.

Credit: Unknown photographer at least to the web. The image is now in the public domain.

Qualitatively, entropy is easy to understand and GENERALIZE to everyday life.

But not its precise formulae.

In fact, most people already have a good understanding of qualitative generalized entropy even if they don't know it.

As disorder increases, so does entropy (the measure of disorder).

And what causes this everyday entropy---random processes.

Just moving about dropping things or laying them anywhere---or dogs and cats marking their territory

Caption: "NICO looks at himself" (2006).

Credit: Georgia Pinaud, Lille , France.

Public domain.

If such RANDOM PROCESSES continued unchecked, your living room would soon be reduced to utter squalor---i.e., a state of high disorder---it's not is it?

At the microscopic level, there are RANDOM PROCESSES increasing to disorder too.

A disorder quantified by entropy---we will not go into formulae here.

But visually we can understand things with the GAS GIF:

Of course, the GAS GIF is completely programmed and repeats.

But it gives the idea of random collisions going on.

Energetically nothing prevents, all the gas molecules in a finite sample from collecting SPONTANEOUSLY in a fraction of volume of a container.

The law of conservation of energy does not forbid it.

Energy can be conserved by all the molecules collecting SPONTANEOUSLY in a fraction of volume of a container.

But that event is never seen to happen.

There are a jillion times more ways that they can be spread out over the whole container than they are ways they can collect SPONTANEOUSLY in a fraction of volume.

There is some 0.00000 ... 0000001 probability that they will---or at least it seems so in principle---but it won't happen anywhere in the observable universe very often---and we can never expect to see that happen---or even something approaching it.

You can press a gas sample into a small volume fraction with a piston, but that takes work.

It does NOT happen SPONTANEOUSLY.

And if the piston returns to its original position, RANDOM PROCESSES lead to the gas sample refilling the whole volume rather quickly.

To give a macroscopic possible impossibility.

You thought it was bad before.

After it's worse.

Even though the tornado had plenty of energy to straighten things up, it never will in human experience.

Caption: "One of several tornadoes observed by the en:VORTEX-99 team on May 3 1999, in central Oklahoma. Note the tube-like condensation funnel, attached to the rotating cloud base, surrounded by a translucent dust cloud."

Tornados are not completely random, but their effects on your living room are rather random---its processes are random relative to your living room.

Permission: Public domain at least in USA.

By creating disorder, RANDOM PROCESSES increase entropy. Which leads us to the second law of thermodynamics.

# The 2nd Law of Thermodynamics

The 2nd law of thermodynamics or---as one can call it: the law of entropy---is:

The 2nd law of thermodynamics is, of course, about the precise entropy of physics. 2nd law of thermodynamics. This entropy is the ``microscopic'' entropy since it is based on microscopic behavior of microscopic particles.

But it qualitative loose sense it also applies to the qualitative generalized entropy of the macroscopic world.

In the qualitative generalized entropy of the macroscopic world, one can't really define maximum entropy unambiguously.

But some states of macroscopic disorder are higher than others.

Second law of thermodynamics together with the rest of thermodynamics has several obviously significant CONSEQUENCES AND/OR CONNECTIONS.

These CONSEQUENCES AND/OR CONNECTIONS are/were understandable and/or well known before/without the second law of thermodynamics. But with second law of thermodynamics they are derivable---NOT that will derive them---from general principles: i.e., those of thermodynamics.

This is often the case in science.

General theories or principles logically precede particulars.

But historically or in personal knowledge, they often follow those particulars.

This is makes perfect sense---as we learn more, we see how things fit together.

To quote T.S. Eliot (1888--1965) completely out of context---but appositely:

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

Now for some of those obviously significant CONSEQUENCES AND/OR CONNECTIONS:

1. Heat will SPONTANEOUSLY flow from HOT (higher T) to COLD (lower T).

HOT and COLD systems are understood in the above statement and are understood to be in THERMAL CONTACT.

When this happens the entropy always increases in the joint system of the HOT and COLD systems.

This can be proven---but we won't even try.

Thus the second law of thermodynamics dictates the HOT-to-COLD rule.

2. Entropy can decrease or increase in an open (or unisolated) system.

Of course for a decrease to happen, the system must be embedded in an environment in which entropy increases enough so that the entropy of the universe increases or at least stays constant.

3. The observable universe is in profoundly NOT in thermodynamic equilibrium as mentioned above.

Light keeps shining out in the darkness.

The Hubble Deep Field.

This is about 1/4 of the original HST deep field image (1995dec18--28): a random empty speck of sky: size here is about 1/60 of a degree: the whole deep field was 2.7 X 2.7 arcminutes.

It is true color (as much as possible) and the blue galaxies must be very blue to still be blue after high redshifts???. There are hundreds of galaxies visible: some the vary faintest are as they were probably only a billion years after the Big Bang. Most may be from 6--9 billion light years or 6--9 billion years in look-back time.

Credit: NASA/HST. This image is the public domain as it was created by and is not otherwise noted as copyrighted.

And we can see the processes---stars blazing away most obviously---by which entropy is trying to increase overall---but not succeeding as we'll get to just below.

Heat is flowing from the interior of the stars with temperatures of millions of degrees on Kelvin temperature scale to cold space.

The temperature of main electromagnetic radiation component in space is, in fact, 2.725 K (or 2.725 kelvins above absolute zero).

This is the temperature of the cosmic microwave background radiation (CMB) that permeates all space and is a relic of the Big Bang.

The flow from hot to cold really started---as far as we can know with any confidence---with the Big Bang.

As the heat flows in its seemingly inexorable journey from hot (Big Bang) to cold (heat death of the universe: see below), little islands of order get created.

This owes to the COMPLEXITY or RICHNESS physical laws.

These little islands are (or at least were once) open systems, of course,

Entropy must increase elsewhere for them to come into existence.

Examples of little islands are galaxies, stars, planets, and the biosphere---which is US writ large.

4. Oddly enough the ultimate state of maximum entropy for observable universe is also one of zero entropy.

As we currently understand things, the expansion of the observable universe is not going to stop.

This causes the average internal energy of space to approach zero in the limit of time going to infinity.

Thus, temperature of the observable universe will approach absolute zero in the limit of time going to infinity.

Since absolute zero is a state of zero entropy (Bloomfield 2006, p. 243), ultimate state of maximum entropy for observable universe is also one of zero entropy.

This whole process has the cheery name of the heat death of the universe.

Of course, our current theory of the observable universe may not last forever.

5. A heat engine working in a cycle between a HOT BATH (OR RESERVOIR) and COLD BATH (OR RESERVOIR) cannot take an amount of heat per cycle from the HOT BATH and turn it into an equal amount of macroscopic work.

Some heat must always be rejected to the COLD BATH.

There is a thermodynamic upper limit in fact on how much heat can be converted to macroscopic work which depends on the ratio of the temperatures of the HOT BATH and COLD BATH.

We will study this limit in some detail in lecture Heat Engines, Refrigerators, and the Carnot Heat Engine (section The Carnot Heat Engine).

A schematic diagram of a heat engine.

Legend

1. The box marked T_H is the hot bath: e.g., burning fuel in the cylinder of an internal combustion engine (ICE).

2. The box marked T_C is the cold bath: e.g., usually the ambient medium. Sometime the ambient medium is present indirectly. Nuclear reactors use water as a cold bath, but the water is cooled in cooling towers to something like the ambient medium.

3. The circle is the working fluid: e.g., the air and burning fuel in the cylinder of an ICE.

4. Q_H is heat absorbed from the hot bath into the working fluid.

5. Q_C is heat rejected from the working fluid to the cold bath.

6. W is the work done by the working fluid.

Credit: Wikipedia contributor Eric Gaba (Sting) . The creator has put the image in the public domain.

The heat engine must reject enough heat per cycle to the COLD BATH so that the overall entropy of the heat engine system does NOT decrease in one cycle.

This consequence of the second law of thermodynamics has frustrated many.

Actual heat engines usually do far less work than the maximum possible.

They have less than the ideal maximum engine efficiency.

We can talk a little about heat engine efficiency here.

```
efficiency = W/Q_H = (Q_H-Q_C)/W

which must always be less than 1 by conservation of energy.

But the

2nd law of thermodynamics

dictates a more stringent limit:

efficiencty = < eff_max = 1-T_C/T_H

where

the temperatures are on the Kelvin temperature scale,

T_C is usually the temperature of ambient medium (e.g., air temperature),

and T_H is usually the temperature of burning fuel.

It's usually hard to do anything about T_C to make it lower.

You can increase efficiency by increasing T_H, but there are practical limits
heat engine
melting.

```
Question: Do you own a large, powerful heat engine?

1. Yes.
2. Maybe.
3. All of the above.

If you own a car or other motor vehicle, you own large, powerful heat engine and are probably even licenced to operate it.

The internal combustion engine is actually NOT a marvel efficiency.

For a steel internal combustion engine, the practical upper limit on efficiency is about 37%.

But that's just the upper limit.

Actual average efficiency of about 18--20%.

But there are other desiderata: safety, power (energy output per unit time), transportability of the high energy density fuel.

The internal combustion engine car has beaten off all competitors for over a century particular electric car which first appear in 1884.

Mainly because internal combustion engine car can transport lots of high energy density fuel (i.e., gasoline) and electric car can't do as well---but things are are changing.

The much higher efficiency of the electric car may lead to its ultimate victory.

In fact, I think the electric car must win---unless the hydrogen car beats it.

6. Similarly a refrigerator (or heat pump) working in a cycle between a HOT BATH (OR RESERVOIR) and COLD BATH (OR RESERVOIR) cannot take an amount of heat per cycle from the COLD BATH and move it to the HOT BATH without some amount of macroscopic work being done.

Enough work must be done so that the overall entropy of the overall refrigerator (which includes the ambient medium) does NOT decrease.

This consequence of the second law of thermodynamics has frustrated many also.

There is a thermodynamic lower limit in fact on how much work is needed to tranfer heat from the COLD BATH to the HOT BATH which depends on the ratio of the temperatures of the HOT BATH and COLD BATH.

We will study this limit in lecture Heat Engines, Refrigerators, and the Carnot Heat Engine (section The Carnot Heat Engine).

Actual refrigerators usually need far more than the minimum possible work to transfer an amount of heat per cycle from the COLD BATH and and move it to the HOT BATH.

They have less than the ideal maximum refrigerator efficiency.

We will study the limit on refrigerator efficiency in lecture Heat Engines, Refrigerators, and the Carnot Heat Engine (section The Carnot Heat Engine).

Caption: "This bubble map shows the global distribution of household refrigerator output in 2000 as a percentage of the top producer (China - 12,790,000 tonnes)".

Public domain.

The second law of thermodynamics is sometimes called arrow of time.

Caption: "A Shoshone man using an arrow shaft straightener."

Credit: SMITHSONIAN INSTITUTION; BUREAU OF AMERICAN ETHNOLOGY BULLETIN 30, HANDBOOK OF AMERICAN INDIANS NORTH OF MEXICO, IN TWO PARTS, PART 1; EDITED BY FREDERICK WEBB HODGE; WASHINGTON, GOVERNMENT PRINTING OFFICE. (1907).

Public domain.

Just as one-way street has an arrow telling which is the only possible direction, so time has its arrow.

Consider an egg dropping on the floor.

The gravitational potential energy of the egg becomes kinetic energy on the fall and on the SPLAT becomes internal energy.

At least in classical physics, one can imagine simply reversing all the microscopic momenta (momentum vectors are mass times velocity) of the egg on the floor plus sound waves spreading out plus any electromagnetic radiation spreading out, and then the whole egg episode would reverse like a film running backwards.

But this reversing is an incredible microscopic re-ordering among the remnants of the splattered egg: entropy would have to undergo a virtually impossible decrease.

Even a little bit off exact reversal for each or most reversed momentum and the egg stays splatted---I think this is a true statement, but some doubt remains.

So we never see splattered eggs reassemble and leap up.

Rubber balls don't have the freedom to splat (i.e., become as disordered as eggs).

They can store the kinetic energy they pick up on being dropped as macroscopic elastic potential energy in the ball and floor.

Then classical physics dictates that they release this stored energy as kinetic energy and you get a bounce.

But the ball never bounces back to its original height.

The energy storage is not ever perfect.

Internal resistive forces in the ball and floor convert some energy to waste heat and thus increase entropy.

The best one can do is with a bouncy ball (superball) that can return to about 80 % of its original height.

The 2nd law of thermodynamics dictates that certain things never happen in reverse time order---the arrow of time thing again.

This is true at the macroscopic level where the a qualitative generalized law of entropy applies as we've argued above with our living room example.

This qualitative generalized law of entropy, includes the well-defined quantitative physics version as a special case as the splattered egg example shows.

Of course, we see lots events repeat and reverse: as, e.g., with a swinging pendulum, driving in and then backing out of a driveway, the planets continuing their quasi-eternal cycles---and in the recreation of memory.

So in a sense there are time repetitions and reversals.

But the reverses and repetitions are limited in physical and temporal scope.

Classical physics dictates the repetitions of pendulums and planets given the right initial conditions and isolation from perturbing effects.

But there always are perturbing effects and pendulums don't cycle forever and even the planet orbits evolve over gigayears.

The steady input of energy in a yearly cycle and the amazing organized complexity of life keeps the biosphere repeating the cycles of life.

But at the level of individual living things there are only limited reversals and repetitions---and species don't repeat.

Caption: "Charles Darwin's 1837 sketch, his first diagram of an evolutionary tree from his First Notebook on Transmutation of Species (1837) on view at the Museum of Natural History in Manhattan."

Credit: Charles Darwin (1809--1882) in 1837.

Public domain.

Biology and consciousness are organizing principles and they slug it out with the 2nd law of thermodynamics (law of entropy) both in its precise form and in its qualitative generalized form.

But they have only a limited concern with repetition and even less with reversal.

The generations of life repeat, but not individual lives: we can back out driveways, but not grow young again---but we are working on that.

There is an actual drug rapamycin (see Ageing: A midlife longevity drug?) that slows mammal ageing---at least in mice.

Rapamycin is already prescribed for humans---as immunosuppresant---which is not so great---live forever---if you don't catch a cold.

Maybe it won't work on humans.

But maybe it will.

Ageing scientists---in both senses of the expression---keep saying they are not trying to find the Fountain of Youth.

So like when they present us with it, they'll claim it was all a big mistake.

I cheer myself up by saying the world's worst dictators will soon be able to live forever.

And, of course, the biosphere and human society evolve because of all kinds of external and internal reasons.

The following is somewhat PHILOSOPHICAL and IDIOSYNCRATIC to yours truly.

But I think that many physicists and scientists would agree with many points.

I think and I think most physicists would agree that the 2nd law of thermodynamics is in a different category from other physical laws.

We can imagine alternative universes where different physical laws apply (particularly laws of force)---and some people do think these alternative universes may exist: see the multiverse.

But everyone thinks the 2nd law of thermodynamics applies in alternative universes: we can't see how it can't.

The apparent necessity of need for the 2nd law of thermodynamics in any physical universe and the existence of qualitative generalized 2nd law of thermodynamics at the macroscopic level, suggests that the 2nd law of thermodynamics can be called emergent principle---a principle that is beyond ordinary physical laws.

Emergent principle is, I think, a common name for the thing. See Wikipedia: Emergence.

There are emergent principles like those of consciousness (whatever that is) and evolution that tend toward order or at least can create order.

Somehow all these principles and physics combine/harmonize to make the observable universe in all of its large and small manifestations.

It's a physical/philosophical question to wonder why the observable universe started (in a Big Bang or by other means) in a sufficiently low state of entropy or high order state to give rise to the little islands of very high order so important to us.

# The 3rd Law of Thermodynamics

First, recall that absolute zero all kinetic energy that can be removed from a system has been removed.

The 3rd law of thermodynamics states:

Caption: Walther Nernst (1864--1941).

Nernst formulated the first version of the 3rd law of thermodynamics.

Credit: Unlisted photographer. Uploaded by User: Magnus Manske in 2007.

Public domain at least in USA.

But there is an interesting point: can absolute zero be reached?

Yes and no.

Individual atoms or molecules can often be at their zero-point energy (that irremovable amount of kinetic energy dictated by quantum mechanics) and, in fact, they often are.

So one can say that they are at absolute zero---if you allow temperature (which is a macroscopic average property) to apply to a single atom or molecule.

But as you make systems larger and larger from a single atom or molecule, both nature and science find it harder and harder to reach absolute zero.

So even for a tiny macroscopic system or large microscopic system, absolute zero may be virtually---if not quite in principle---impossible.

The current laboratory record low temperature for a sample of size above atomic is currently 1*10**(-10) K (in a limited sense) set in 2000 (Wikipedia: Absolute zero).

# Phases of Matter

A phase is macroscopic state of a substance (a material with definite chemical composition) with relatively uniform physical and chemical properties.

Changes between a substance phases alone do not involve chemical changes since the substance stays chemically the same.

Thus, phase changes are called PHYSICAL CHANGES as distinct from CHEMICAL CHANGES.

However, the distinction of a PHYSICAL CHANGE from a CHEMICAL CHANGE is not so great in principle since in both cases there are changes in the chemical bonds (defining chemical bonds broadly).

There are three main phases of matter: solid, liquid, gas.

There are some other phases. Most are rather delicate phases that are of great interest in physics and sometimes technology, but don't appear obviously in everyday life. And strange phases of various sorts exist in extreme conditions in the universe.

Plasma (in the physics sense of the word) is often consider a fourth important phase.

It is a gas of ionized atoms.

Ions are atoms that have gained or lost electrons, and so are electrically charged.

But plasmas are neutral overall, because the charge separations are on a small physical scale.

But some of us just think of ionized gases as gases of ions, and thus think of plasmas as just a kind of gas.

Caption: "This is an illistation created by me on MS paint on the phase changes of a system. Nomenclature is also included".

Credit: User: Penubag in 2007.

Public domain.

Question: The least dense phase at a given temperature and pressure is usually:

1. gas.
2. liquid.
3. solid.
4. None of the above.

This must be true almost always, but there may be some strange counterexamples.

Let us now discuss the (main) phases of matter in turn.

1. Solids

In solids, the atoms or molecules are bonded by fairly rigid chemical bonds.

Chemical bonds include ionic and covalent bonds and weaker kinds of bonds.

The bonds are not completely rigid since the atoms or molecules can vibrate because of kinetic energy and can be bent or broken by applied forces.

Some solids have regular crystal structure.

But this regular structure usually extends only over a small region called a grain or crystallite.

The crystallites are fused together in irregular bonded regions to make largish samples of solids.

Crystallites typically are a few nanometers to a few millimeters in size scale.

Caption: "Galvanized surface with visible crystallites of zinc. Crystallites in the steel under the coating are microscopic."

The caption is not too informative, but the crystallite size scale may be 5 mm.

Galvanization in this context means coating with zinc to prevent corrosion.

Credit: User: Splarka in 2005.

Public domain.

A few much larger crystallites exist: e.g., large gem stones or specially manufactured samples.

Some solids are amorphous solids have no long-range crystalline structure and the chemical bonding is somewhat irregular.

Glass is the common example of an amorphous solid: by mass it primarily silicon and oxygen like most rock.

The atoms in solids are tightly packed.

Atoms have no definable sharp surface, but they have a region of strong interaction and in solids these regions are in contact.

It takes great pressure to force atoms closer together than their radius of strong interaction.

Such pressures do exist in the interior of planets, stars, and other dense strongly-self-gravitating astro-bodies.

The Earth's centeral pressure is about 350 GPa (3.5*10**11 Pa = 3.5*10**6 atmospheres) (Wikipedia: Inner core). But the density of the iron there is only about 13 g/cm**3 (The Interior of the Earth, Eugene C. Robertson). This is seemly not much larger than under room pressure: 7.874 g/cm**3.

The density is only a bit lower in vacuum---but how much?

Earth air pressure is tiny for solids.

Going from a vacuum to 15 psi and the contraction of solids is very small though measurable.

The reverse is also true solids do not expand much when pressure is lowered from Earth air pressure to zero.

2. Liquids

Liquids are usually nearly as dense as solids, and so are tightly packed.

They show weaker bonding between the particles (atoms or molecules) and the bonds to nearest neighbors change with small applied force (Bloomfield 2006, p. 216)

Because of the tight packing liquids resist compression and decompression much like solids.

But under sufficiently low pressure, liquids have a strong tendency to evaporate.

But because of the weak bonding, the particles slid fairly freely over each other.

Thus liquids flow.

Liquids and gases are collectively called fluids because they flow.

Plastic solids can also be considered fluids though they tend to flow slowly---the Earth's mantle very slowly.

Convection in the asthenosphere driving plate tectonics.

The convection cells extend throughout the mantle.

Convection occurs whenever you have fluid (in some sense) and a strong enough temperature gradient.

It happens in the Earth's atmosphere, in the Earth's interior, in stars, and in a boiling pot of water.

Credit: U.S. Geological Survey (USGS). Their images are mostly public domain.

An ideal fluid (which includes the case of ideal liquid and ideal gas) cannot resist a shearing force: i.e., a force that tries to change its shape, but not its volume.

Of course, actual liquids show range of viscosity (resistance to shear).

3. Gases

In gases the particles (molecules and/or atoms) are not bound and are well spread apart.

On Earth most gases are composed of molecules which are set groupings of bonded atoms: e.g., N_2, O_2, CO_2.

The Noble gases such as helium and argon are monatomic gases (i.e., gases with the particles consisting of single atoms).

The particles interact through collisions which give rise pressure.

Unlike solids and liquids, gases expand and contract easily with pressure because they are NOT tightly packed.

Actually for all ordinary gases, at constant temperature,

```

Pressure is proportional to 1/Volume

```
to some approximation which is a result that follows from the ideal gas law.

# Phase Changes

Bulk phase changes (or transitions) for a pure substance happen at definite temperatures which---just to make life complicated---are dependent on pressure.

To get a phase change at the temperature specified for the material, the sample must have the constant temperature in space as the transition occurs.

If there are a range of temperatures in the sample, then the situation is more complex obviously.

Nevertheless, in many typical and not well-controlled cases, the bulk phase changes will happen at nearly the temperatures specified for the material.

The order of changes with increasing temperature is solid to liquid to gas.

The change (reverse change) from solid to liquid is melting (freezing).

The change (reverse change) from liquid to gas is evaporation (condensation).

The direct change (direct reverse change) from solid to gas is formally sublimation (deposition).

Actually many people---like yours truly and other astrophysicists---loosely use evaporation and condensation for, respectively, sublimation and deposition.

The phase change temperatures generally INCREASE with increasing pressure.

It is a good mnemonic to say that increased pressure usually likes to keep matter in the usually denser phase.

This is true loosely speaking.

The higher the pressure increases the strength of the chemical bonds and a higher temperature (implying greater microscopic kinetic energy) is required to break/change the bonds.

Of course, then phase change temperatures generally DECREASE with decreasing pressure.

This is actually a problem if you want really hot coffee at high altitude.

Water boils at 100 degrees C (373 K) at standard pressure (about 0.1 MPa). On the peak of Mount Everest the pressure is about (0.026 MPa) and the boiling point of water is only about 69 degrees C (342 K) ( Wikipedia: Boiling Point).

Once water starts boiling it won't get any hotter than the boiling point since all the added internal energy goes into evaporating the water as we will discuss below.

Unless boiled under pressure, real hot coffee is difficult at high altitude.

``Yes sir, nothing like lukewarm coffee after a day of climbing in sub-freezing conditions in a blizzard.''

Of course, you could take your own espresso machine with you on the ascent.

Under sufficiently low pressure, the whole liquid phase gets skipped and a solid will phase change directly to a gas.

What low pressure depends on the substance.

Most familiar substances have a liquid phase under ordinary air pressure.

There as some noteworthy ones that do NOT.

There is another extreme case of pressure.

At very high pressures the distinction between liquids and gases vanishes.

You know longer see an interface between the denser and less dense parts of what can be just called the fluid phase.

It takes significant internal energy to break the chemical bonds when a sample is undergoing a phase change.

Question: Melting a sample of ice takes about as much energy as raising liquid water's temperature by ____________ degrees Celsius.

1. 80
2. 1
3. 800
4. All of the above.

```
specific latent heat of fusion / specific heat

=   333 kJ/kg / 4.190 kJ/(kg C) = approximately 80 C.

```

Adding internal energy when a sample is undergoing a phase change tends to go into breaking the bonds chemical bonds and not into increasing temperature.

If you added the internal energy very uniformly and slowly to the sample, you could keep the whole sample at the phase change temperature and have all the added internal energy go into breaking the chemical bonds: i.e., into causing the phase change.

It's hard to arrange this to happen perfectly, but not so hard to do it approximately.

This is why the liquid water in ice water tends to stay ice-cold: i.e., near the freezing temperature of water (at about 0 degrees C = 273.15 K, but there is some pressure dependence) as long as any ice persists in the sample.

This is also why boiling water won't get hotter than boiling temperature.

Virtually all the added internal energy goes into breaking the chemical bonds.

Only after all the liquid water is gone will the inside of the container be able to get much hotter than the boiling point.

This, of course, is why it is hard to get hot coffee on the peak of Mount Everest as mentioned above.

Ice undergoing a phase change to water at approximately a constant overall temperature near 273.15 K = 0 degrees C.

The lemon is essentially a bystander---but decorative.

Credit: Jon Sullivan of PD Photo.org. The author has released the image into the public domain.

Now the melting and boiling temperatures are the melting and boiling for bulk samples where the samples are all at the same temperature for the ideal behavior.

At the surface of any surface of any sample of solid or liquid, the individual atoms or molecules have a distribution of thermal energies.

There will always be some atoms or molecules that can break chemical bonds and escape from the surface.

But atoms or molecules in the phase of escape can also land on the surface and rebond if their individual thermal energies are low.

There is, in fact, a continual flow of escapees and returnees at surfaces.

For example, at the surface of a liquid, if the gross evaporation rate exceeds the gross condensation rate, there will be a net evaporation rate and the sample of liquid will evaporate even at temperatures well below the boiling temperature.

The rates of escape and return depend on many things, but a key one is the density of the atoms or molecules in the phase of escape.

We see this all the time with water: samples of water evaporate as long as the relative humidity is less than 100 %.

Just as evaporation can happen well below the boiling temperature, so sublimation can happen will below the melting temperature.

We have all seen this with ice and snow.

It vanishes even if the temperature stays sub-freezing.

Especially if the there is bright sunlight (in other words radiant energy) to give internal energy.

Ice surfing on the Znin Small Lake.

See Znin, Poland.

Ice forms on the top of water bodies, because it is less dense than liquid water.

Usually the solid phase is denser than the liquid.

That this is not so for water is one of water's remarkable properties.

At 0 degrees C, ice has density density 0.9167 g/cm**3 but liquid water has density 0.9998 g/cm**3. Liquid water density reaches a maximum of 1.00 g/cm**3 at 4 degrees C ( Wikipedia: Ice). These precise numbers are for a air at 1 atmosphere air pressure (0.101325 Mpa) (I think).

As liquid water passes below 4 degrees C it becomes more buoyant than warmer water (because less dense) and tends to rise and reach the surface where it freezes or it could freeze and float to the surface.

Icebergs float likewise because ice is less dense than liquid water.

Credit: Wikipedia contributor Andrej Luczak. According to Wikipedia permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version.

It is possible to see all three (main) phases of matter at once.

But this will not be a system in overall thermodynamic equilibrium usually.

It will be a state of thermodynamic non-equalibrium which means that the system will changing in time or will be in some steady state with inflows and outflows of energy and/or matter in some form.

For example, we do see the three phases of water at the same time in a system---cough---not in thermodynamic equilibrium When evaporation happens from surfaces below the boiling temperature, there is a strong cooling effect.

Evaporative cooling occurs because the evaporation process takes significant internal energy from the surroundings in order to cause the escape of the atoms or molecules.

Evaporative cooling is a vital process in making refrigerators work as we will discuss in lecture Heat Engines, Refrigerators, and the Carnot Heat Engine (section Refrigerators).

Evaporative cooling is also important to life.

Mammals, for example, can cool by sweating.

Water is emitted from the skin and evaporates causing a cooling effect.

Humans are the grand champion sweaters, in fact.

Our maximum water perspiration rate is over 500 g/(m**2*h) (Smil 2006, p. 61).

Our sweat potential gives humans a tremendous ability to be active and work while most other mammals and other critters are flaked out.

In South African gold mines, miners at 3 km down work in temperatures of 50 degrees C (Smil 2006, p. 61).

Workers in 18--19th century iron foundries may have endured similar temperatures (Cardwell 1994, p. 171): they worked in the Inferno.

Caption: "Dante's guide rebuffs Malacoda and his fiends in Inferno Canto 21 between ditches five and six in the eight circle."

Credit: Gustave Dore (1832-1883).

Public domain.

Other mammals are way down. Camels---those ships of the desert---max out at about 250 g/(m**2*h). Horses can do about 100 g/(m**2*h).

And then there are canids.

The Irish wolfhound who is the mascot of Irish Guards who are evidently in the British Army.

The Irish wolfhound is the tallest breed of dog with an average height at the withers of 90 cm (34 inches).

Canids (which include dogs) don't sweat (or so my source tells me).

They pant and tongue-loll to make use of evaporative cooling from the somewhat inner surfaces of their bodies (Smil 2006, p. 61).

Credit: Wikipedia contributor Elf. According to Wikipedia permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version.