2. Thermal Physics

1. Heat & Temperature1. Temperature2. Thermal Expansion3. The Atomic Nature of Matter4. Gas Laws5. Kinetic-Molecular Theory6. Phases

2. Calorimetry1. Sensible Heat2. Latent Heat3. Chemical Potential Energy

3. Heat Transfer1. Conduction2. Convection3. Radiation

4. Thermodynamics

“Heat and Temperature”TEMPERATURE

Internal Energy The energy due to the coordinated motion (kinetic energy) and average position

(potential energy) of a large collection of particles is usually known as mechanical energy, but is sometimes called external energy.

The sum of the energies due to the random motion (kinetic energy) and local position (potential energy) of a large collection of particles is known as its internal energy.

The symbol for internal energy is U. The SI unit for internal energy is the joule [J].

Heat Two regions that can exchange internal energy are said to be in thermal contact. The net transfer of internal energy between two regions in thermal equilibrium is zero. Heat is the net transfer of internal energy from one region to another. The symbol for heat is Q (probably from "quantity of heat"). The SI unit for heat is the joule [J].

Temperature Temperature can be defined informally as the measure of a region's "hotness".

A region which is "hot" has a higher temperature than one that is "cold". Two regions have the same temperature when there is no net exchange of internal energy

between them. Heat flows from one region to another due to a difference in temperature. (Heat

flows from "hot" to "cold".) No heat flows between two regions with the same temperature.

The symbol for temperature is T. A device that can be used to measure temperature is called a thermometer.

All thermometers measure the value of some thermometric variable that responds to changes in temperature.

Thermometers can be classified according to the thermometric variable measured. A temperature scale is built from…

at least two fixed points (an upper fixed point and a lower fixed point) corresponding to the temperatures of a pair of reproducible experiments and…

a fundamental interval or span of numbers between the two fixed points. The SI unit of temperature is the kelvin [K].

Symbology In current usage, the kelvin is always written in lowercase letters without a

degree symbol [K]. In some early Twentieth Century sources it was common to see degree Kelvin

[°K], but this is no longer considered acceptable. The kelvin is a fundamental unit; that is, it cannot be reduced to any simpler units. By definition, the kelvin is 1/273.16 of the thermodynamic temperature of the triple

point of water; therefore… the triple point of water is the upper fixed point, absolute zero is the lower fixed point, and 273.16K is the fundamental interval of the kelvin temperature scale.

The degree Celsius [ ] is an acceptable non SI unit for temperature. ℃ Symbology

The reversed phrase Celsius degree [C°] is sometimes used for temperature intervals (ΔT).

The original name for this unit was the degree centigrade [ ], but this is no ℃longer considered acceptable.

The current definition of the degree Celsius is 1/273.16 of the thermodynamic temperature of the triple point of water like the kelvin, but…

the triple point of water is assigned the value 0.01 and ℃ absolute zero is assigned the value −273.15 . ℃

The original definition of the degree Celsius is still valid with… the normal boiling point of water as the upper fixed point, the normal freezing point of water as the lower fixed point, and 100 as the fundamental interval. ℃

The degree Celsius and kelvin have the same size, but assign zero to different values. ΔT [K] = ΔT [ ]℃

T [K] = T [ ] + 273.15℃T [ ] = ℃ T [K] – 273.15

THERMAL EXPANSIONThermal expansion refers to a fractional change in size of a material in response to a change in temperature.

This includes… changes in length compared to original length (Δℓ/ℓ0) called linear expansion

changes in area compared to original area (ΔA/A0) called areal expansion or superficial

expansion changes in volume compared to original volume (ΔV/V0) called volumetric expansion or

cubical expansion For most materials, over small temperature ranges, these fractional changes…

are directly proportional to temperature change (ΔT) and have the same sign (i.e., materials usually expand when heated and contract when

cooled) are larger for liquids than solids

A coefficient of thermal expansion… is the ratio of the fractional change in size of a material to its change in temperature is represented by the symbol α (alpha) for solids and β (beta) for liquids uses the SI unit inverse kelvin (K−1 or 1/K) or the equivalent acceptable

non SI unit inverse degree Celsius (℃−1 or 1/ ). ℃ Solids…

tend to retain their shape when not constrained and so are best described by a linear coefficient of thermal expansion, α (alpha).

have an areal expansion that is very nearly twice their linear expansion, 2α(since two perpendicular linear measurements describe an area)

have a volumetric expansion that is very nearly three times their linear expansion, 3α(since three perpendicular linear measurements describe a volume)

Liquids… tend to take on the shape of their container and so

are best described by a volumetric coefficient of thermal expansion, β (beta). Gases…

have a thermal expansion that is best described using the ideal gas law described later in this book.

ATOMIC NATURE OF MATTEROrdinary matter (as opposed to dark matter) is mostly composed of atoms.

Atoms… are discrete entities.

A discrete system is composed of distinct individual parts. A discrete system is separable into pieces.

The opposite of discrete is continuous. A continuous system forms an unbroken whole without interruption. One region blends seamlessly into another.

can only be found in a limited number of basic types called elements (short for chemical elements).

There are 90 naturally occurring elements found on earth. An additional 28 elements have been produced artificially in laboratories on

earth. A few elements that exist on earth only in the laboratory have been detected in

stars other than the sun. can be stable or unstable.

Unstable atoms have a finite existence. There is a statistical probability that an unstable atom will decay into an atom of

a different element. Stable atoms are eternal.

The stable atoms of everyday existence are several billion years old. Nearly all of the hydrogen and helium in the universe was created in the

first three minutes of the universe's existence (13.8 billion years ago). Nearly all of the elements heavier than helium found on the Earth were

created many millions of years before the solar system formed (4.5 billion years ago).

Stable atoms can be used over and over again (recycled) in different combinations and will never "wear out".

can be "seen" only with great difficulty. Atoms are effectively "invisible".

Atoms are on the order of 10−10 m in size. Light waves are on the order of 10−6 m in size. Since light is 10,000 times larger than atoms, atoms are too small to be "seen"

with light. (No optical device can ever be used to image atoms.) Atoms can be inferred to exist through…

the chemical laws of definite and multiple proportions. the physical laws of statistical thermodynamics.

Atoms can be imaged through… x-ray diffraction scanning tunneling electron microscopy atomic force microscopy

Atoms can combine to form… ionic solids network solids metallic solids molecules

GAS LAWSThe basic gas laws for a constant amount of matter… pressure–volume (constant temperature)

The pressure of a gas is inversely proportional to its volume when temperature is constant.

The product of pressure and volume is constant when temperature is constant. This relationship is known as Boyle's law or Mariotte's law. A constant temperature process is said to be isothermal.

volume–temperature (constant pressure) The volume of a gas is directly proportional to its temperature when pressure is constant. The ratio of volume to temperature is constant when pressure is constant. This relationship is known as Charles' law or Gay-Lussac's law. a constant pressure process is said to be isobaric.

pressure–temperature (constant volume) The pressure of a gas is directly proportional to its temperature when volume is constant. The ratio of pressure to temperature is constant when volume is constant. This relationship is not associated with any particular scientist. A constant volume process is said to be isochoric.

Avogadro's hypothesis The number of molecules in a given volume of gas at a given temperature is the same for all

gases. The ideal gas law (presented two ways)… functional thermodynamics

PV=nRT statistical thermodynamics

PV=NkT

Thermodynamic changes with special names… An isobaric process is one that takes place without any change in pressure. An isochoric process is one that takes place without any change in volume. An isothermal process is one that takes place without any change in temperature.

Isothermal processes are often described as "slow".

The pressure of a gas is inversely proportional to its volume only if the change takes place isothermally.

An adiabatic process is one that takes place without any exchange of heat. Adiabatic processes are often described as "fast". The pressure of a gas is not inversely proportional to its volume if the change takes place

adiabatically.

KINETIC-MOLECULAR THEORYThe kinetic–molecular theory (kmt)…

is a theory of ideal gases can be used to deduce the properties of gases can be applied to other systems such as free electrons in a metal is sometimes called the molecular–kinetic theory (mkt)

Postulates All matter is composed of particles (molecules in general, but also atoms, ions, and free

electrons). Molecules are very small relative to the distance between them. Molecules are in constant random (chaotic) motion. Collisions between molecules are perfectly elastic.

Equipartition of Energy The time-averaged kinetic energy of the molecules in a gas…

is divided equally among all the possible degrees of freedom For a monatomic gas, there are 3 degrees of freedom, one for each spatial

direction (x, y, z) For a monatomic gas, there are 5 degrees of freedom, one for each spatial

direction (x, y, z) plus one for each rotational axis (θ, φ). is equal for every kind of molecule in a mixture of gases On average, heavier molecules move slower and lighter molecules move faster.

A proper discussion of kmt includes statistics. Time-averaged quantities are written in angle brackets,

Pressure Absolute pressure is the time-averaged rate per unit of area at which momentum is changed

when the molecules of a gas collide with the walls of its container. Temperature

Absolute temperature is proportional to the time-averaged kinetic energy of the molecules in a

gas, ⟨K⟩∝T.

Molecular speeds are described by the Maxwell-Boltzmann distribution. The curve of the Maxwell-Boltzmann distribution…

resembles a bell curve

has no negative values has a positive skew (most values are greater than the most probable value) has a total area under the curve of 1

The probability of finding a molecule with a speed in a certain range is equal to the area under the that section of the curve.

The most probable speed occurs at the maximum value of the distribution. Higher temperature shifts the peak of the curve…

"right" — higher temperature increases the most probable speed "down" — higher temperature increases the statistical dispersion (the curve is flatter and

wider) The measures of central tendency are not all the same (vp<⟨v <⟩ vrms).

PHASES

solid definite volume and shape high atomic order

liquid definite volume, indefinite shape moderate and transitory atomic order

gas indefinite volume and shape no atomic order

glass plasma

indefinite shape and volume a gas of electrons and ions

metal definite shape and volume a gas of electrons, a solid of ions

polymorphs and allotropes There are often several ways to arrange the particles of a substance. These variations are called polymorphs or allotropes.

phase changes melting, freezing, fusion boiling, evaporation, vaporization, condensation

Equilibrium can be used to describe two very different situations. Static equilibrium occurs whenever the components of forces and torques acting in one

direction are balanced by the components of forces and torques acting in the opposite direction.

A system in static equilibrium will have a constant translational and angular velocity.

Dynamic equilibrium occurs whenever a change in the statistical behavior of a large group of particles is balanced by an opposite change in the statistical behavior of a similarly large group of different particles.

A system in dynamic equilibrium will have a constant mass, pressure, temperature, and volume.

Dynamic equilibrium is a state where no macroscopic change is observed. Phase changes occur whenever a large group of particles is out of dynamic equilibrium.

The dynamic equilibrium phase plotted on a pressure-temperature graph is called a phase diagram.

Each substance has its own characteristic phase diagram. The lines separating phases on a phase diagram are known as phase boundaries.

liquid-gas The liquid-gas phase boundary is known as the vaporization curve or

vapor pressure curve. The value of the liquid-gas phase boundary at a given pressure is a

boiling point. The value of the liquid-gas phase boundary at atmospheric pressure is the

normal boiling point The liquid-gas phase boundary terminates at a critical point with a critical

pressure and critical temperature. A gas cannot be liquefied by compression if it is hotter than its

critical temperature. It will remain a gas. solid-liquid

The solid-liquid phase boundary is known as the fusion curve or melting curve.

The value of the solid-liquid phase boundary at a given pressure is a melting point (or freezing point).

The value of the solid-liquid phase boundary at atmospheric pressure is the normal melting point (or normal freezing point).

solid-gas The solid-gas phase boundary is known as the sublimation curve. The value of the solid-gas phase boundary at a given pressure is a

sublimation point. The value of the solid-gas phase boundary at atmospheric pressure is the

normal sublimation point. The point where three phase boundaries meet is a triple point.

All three phases exist in dynamic equilibrium when a substance is at its triple point.

A gas cannot be liquefied by cooling if the pressure is less than the triple point pressure. It will go directly to the solid phase.

“Heat Transfer”LATENT HEAT

All phase changes… take place at a specific temperature and for a given pressure. take place without a change in temperature. (There is no temperature change during a

phase change.) involve changes in internal potential energy. release or absorb latent heat.

Endothermic phase changes absorb heat from the environment. (They are cooling processes.)

Exothermic phase changes release heat to the environment. (They are warming processes.)

The specific latent heat (L) of a material… is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase

change. is defined through the formula Q=mL. is often just called the "latent heat" of the material. uses the SI unit joule per kilogram [J/kg].

There are three basic types of latent heat each associated with a different pair of phases.

CONVECTIONConvection is the transfer of heat by the flow of a fluid.

Spontaneous convection… is caused by the boyancy differences between

warmer, less dense fluid and cooler, more dense fluid

is also caused by differences in surface tension between hotter regions with less surface tension and cooler regions with more surface tension

can be summarized in two simple rules hot fluid rises cold fluid sinks

will result in the formation of closed loops of circulating fluid called convection cells Forced convection…

is aided by fans, blowers, impellers, lungpower, etc. is described by newton's law of cooling

THERMODYNAMICSThermodynamics - the science that is concerned with energy, particularly ‘energy-in-transit’ in the forms of heat and work, and those properties of systems that are related to energy.

Energy – the ability to do work. All energy is relative! Energy-in-transit is not relative.

Three kinds of energy:(1) potential - energy due to relative position,(2) kinetic - energy due to relative velocity,(3) internal - the sum of all potential and kinetic energies of constituent parts [atoms, molecules, etc.] of a system.

Two kinds of ‘energy-in-transit’:(1) heat – energy transferred between system and surroundings because of a temperature difference, or gradient.(2) work - energy transferred between system and surroundings because of a pressure difference, or gradient.

Thermodynamic System – just “the thing” that we are talking about! Everything else is called the surroundings. The sum of the system and the surroundings is the universe.Three kinds of systems:

(1) closed system – a fixed quantity of material; energy can cross the system boundaries but mass can not.(2) open system – a particular region of space; both mass and energy may cross the system boundaries.(3) isolated system (not an important concept) – neither energy nor mass may cross the system boundaries.

In elementary thermodynamics all systems consist only of atoms and molecules where the net electric charge of the system is zero. In addition, all electrical and magnetic and surface forces are generally neglected.

Thermodynamic Materials - Systems composed of atoms and molecules are called materials.Two kinds of materials:

(1) pure materials - composed of only one molecular species, and(2) mixtures - composed of two or more molecular species.

ideal mixtures - mixtures where the volume and enthalpy of the mixture are simply the sums of the volumes and enthalpies of the pure components at the temperature and pressure of the mixture.  Elementary thermodynamics deals only with ideal mixtures. Advanced thermodynamics is concerned with non-ideal mixtures, in phase equilibrium and reaction equilibrium.

Four basic concepts of materials:(1) Quantity

(a) mass (or weight in a known gravitational field) (b) number of objects (one gram mole = 6.025 x 10^23 objects)

mean-molar-mass (molecular weight or atomic weight) is the mass of one mole of a particular collection of objects, and is the constant which allow conversion between these two measures of quantity.(2) Composition of a mixture

(a) fraction - quantity of a particular species per unit quantity of the mixture.(b) concentration - quantity of a particular species per unit volume of the mixture.

(3) Phase - a homogeneous quantity of material, characterized throughout by a single set of thermodynamic properties.

(a) solids - materials which are capable of resisting shear stresses.(b) fluids - materials which exhibit continuous deformation under shear stress. (c) liquids - fluids which can conform to their containers without occupying them completely.(d) gases - fluids which conform to and completely occupy their containers.(e) vapors - gases at temperatures less than their critical temperature.

quality - ratio of quantity of vapor to the total quantity of material [vapor & liquid] or [vapor & solid] in a system

(4) State - defined by the properties of a material.(a) subcooled liquid (or compressed liquid) - a liquid at a temperature below its saturation temperature or at a pressure above its saturation pressure.(b) superheated vapor - a vapor at a temperature above its saturation temperature or at a pressure below its saturation pressure.

(c) saturated - if two or more phases exist within a system at equilibrium, the system is said to be saturated and all phases present are saturated. In particular, if vapor and liquid phases are both present within a system, the vapor is said to be saturated vapor and the liquid is said to be saturated liquid

Thermodynamic Properties - any quantity that depends only on the state of a material and is independent of the process by which a material arrives at a given state.Properties of a System - the average or homogeneous properties of a system at equilibrium.

Two kinds of properties:(1) intensive - independent of the quantity of material [T, P, Cp and Cv], and all specific and molar properties.(2) extensive - directly proportional to the quantity of material [V, S, U, H, etc.].

Pseudointensive properties - extensive properties expressed per unit quantity of material [v, s, u, h, etc.].

Two kinds of pseudointensive properties:(1) specific properties - expressed on a unit mass basis, and(2) molar properties - expressed on a unit mole basis.

Five basic thermodynamic properties:(1) temperature [T] (thermal potential) - a measure of the relative hotness or coldness of a material.(2) pressure [P] (mechanical potential) - the normal (perpendicular) component of force per unit area.(3) volume [V] (mechanical displacement) - the quantity of space possessed by a material.(4) entropy [S] (thermal displacement) - the quantity of disorder possessed by a material.(5) internal energy [U] - the energy of a material which is due to the kinetic and potential energies of its constituent parts (atoms and molecules, usually).

Two secondary thermodynamic properties:(1) enthalpy [H] - internal energy plus the pressure-volume product.(2) heat capacity [Cp or Cv] (specific heat) - the amount of energy required to increase the temperature of one unit quantity of material by one degree, under specific conditions.

(a)constant pressure Cp = dh/dT(b)constant volume Cv = du/dT

Gibbs Phase Rule: F = 2 + Ns – Np

F - degrees of freedom of the system = the number of independent, intensive thermodynamic variables (properties or compositions) which must be specified to fix the intensive state of the system,Ns - number of molecular species within the system, andNp - the number of phases within the system.

Thermodynamic Processes and Cyclesprocess - any succession of events.chemical process - a chemical or physical operation, or series of operations, which transforms

raw materials into products.thermodynamic process - the path of succession of states through which the system passes in moving from an initial state to a final state.polytropic process - a thermodynamic process for which [PVn] is constant. These processes are usually associated only to systems for which the ideal gas assumption holds.

Four special polytropic processes:(1) isobaric - - - - - - - constant pressure [n = 0](2) isothermal - - - - - - constant temperature [n = 1](3) isentropic - - - - - - constant entropy [n = gamma,(Cp/Cv)](4) isochoric (isometric) - constant volume [n = infinity]

Two other important processes:(1) adiabatic - no heat transfer.(2) isenthalpic - constant enthalpy.  This is the same as isothermal for an ideal gas system.

reversible process – an idealized process in which the deviation from thermodynamic equilibrium is infinitesimal at any particular instant during the process. All of the states through which a system passes during a reversible process may be considered to be equilibrium states. This is an idealized situation that would require infinite time and/or equipment size to be realized. The concept of a

reversible process serves to set a maximum for the efficiency of a given process. Note that an isentropic process is an adiabatic-reversible process, so that real isentropic processes are not possible.

thermodynamic cycle - a process for which the final and initial states are the same.

Four common ‘idealized’ thermodynamic cycles:(1) Carnot cycle - isothermal and isentropic compressions followed by isothermal and isentropic expansions.(2) Rankine cycle - isobaric and isentropic compressions followed by isobaric and isentropic expansions.(3) Otto cycle - isentropic and isochoric  compressions followed by isentropic and isochoric expansions.(4) Diesel cycle - isentropic compression followed by isobaric, isentropic and isochoric expansions

Thermodynamic LawsA physical law is a simple statement of an observable physical phenomenon that has no

underlying, more-basic reason for being except that the most accurate observations have always proved it to be true.

Zeroth law of thermodynamics – If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

First law of thermodynamics – Energy can neither be created nor destroyed. It can only change forms. In any process, the total energy of the universe remains the same. For a thermodynamic cycle the net heat supplied to the system equals the net work done by the system.

Second law of thermodynamics – The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

Third law of thermodynamics – As temperature approaches absolute zero, the entropy of a system approaches a constant minimum.