Chapter 17:Thermal Properties

Thermal Properties

• Heat capacity• Specific Heat• Thermal Energy Mechanism• Coefficient of Thermal Expansion• Thermal Conductivity• Thermal Stresses• Thermal Shock• Applications where these parameters are

significant

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Thermal Energy• The energy needed to raise the temperature of an object

depends on the mass and composition of the object. • The heat capacity measures the combined effect of mass

and composition. Heat capacity, C, as distinct from specific heat capacity, is the measure of the energy required to increase the temperature of an object by a given temperature interval. Heat capacity is an extensive property dependent on the amount of material.

• The specific heat, c, or specific heat capacity, is a property of the composition only. It measures the energy required to increase the temperature of a unit quantity of a specific substance by a specific temperature interval.

• An object's temperature is a measure of the random molecular motions. Individual atoms and molecules are never still. 3

Atomic Vibrations

• Faster molecules striking slower ones at

the boundary in elastic collisions will

increase the velocity of the slower ones and

decrease the velocity of the faster ones,

transferring energy from the higher

temperature to the lower temperature

region. • With time, the molecules in the two

regions approach the same average kinetic

energy (same temperature) and in this

condition of thermal equilibrium there is no

longer any net transfer of energy from one

object to the other.

• The atoms and ions that are bonded together with considerable interatomic forces, are not motionless.

• Due to the consistent vibrating movements, they are permanently deviating from their equilibrium position.

•Atomic vibrations are in the form of lattice waves or phonons.

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• Quantitatively: The energy required to produce a unit rise in temperature for one mole of a material.

heat capacity(J/mol-K)

energy input (J/mol)

temperature change (K)

Heat Capacity

• Two ways to measure heat capacity:Cp : Heat capacity at constant pressure.

Cv : Heat capacity at constant volume.Cp usually > Cv

• Heat capacity has units of

Fmollb

Btu

Kmol

J

dT

dQC

The ability of a material to absorb heat.

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incr

eas

ing

cp

• PolymersPolypropylene Polyethylene Polystyrene Teflon

cp (J/kg-K)at room T

• Ceramics

Magnesia (MgO)Alumina (Al2O3)

Glass

• MetalsAluminum Steel Tungsten Gold

1925 1850 1170 1050

900 486 138 128

cp (specific heat): (J/kg-K)

Material

940 775

840

Specific Heat: Comparison

Cp (heat capacity): (J/mol-K)

More heat energy is required to increase the temperature of a substance with high specific heat capacity than one with low specific heat capacity. For instance, compare the specific heat energy required to increase the temperature of glass (cp = 840 J/kg-K) with that required for gold of the same mass (cp = 128 J/kg-K) .

The symbols for specific heat capacity are either C or c depending on how the quantity of a substance is measured.

Internal Energy Comparison

• When the sample of water and copper are both heated by 1°C, the addition to the kinetic energy is the same, since that is what temperature measures.

• But to achieve this increase for water, much more energy must be added to the potential energy portion of the internal energy.

• So the total energy required to increase the temperature of the water is much larger; its specific heat is much larger.

Lorentz ConstantLorentz constant relates electrical and thermal

conductivity.

The Lorentz constant is proportional to the ratio of the thermal conductivity to the electrical conductivity: L = k/σT

For example, if the electrical conductivity of aluminum is 3.8 x107/ Ωm, estimate it's thermal conductivity (Lorentz constant from Table 17.1).

Thermal conductivity: k = σLT = LT/ρ; (T = 293K)

Given k = 245 W/m K

Thermal Expansion Effects

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• The most easily observed examples of thermal expansion are size changes of materials as they are heated or cooled.

• Almost all materials (solids, liquids and gases) expand when they are heated and contract when they are cooled.

• Increased temperature increases the frequency and magnitude of the molecular motion of the atoms and produces more energetic collisions.

• Increasing the energy of the collisions forces the molecules further apart and causes the material to expand.

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Thermal Expansion

Length increases when temperature increases.

)(α initialfinalinitial

initialfinal TT

linear coefficient ofthermal expansion (1/K or 1/°C)

Tinitial

Tfinal

initial

final

Tfinal > Tinitial

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Coefficient of Thermal Expansion: Comparison

Why does generally decrease with increasingbond energy?

Polypropylene 145-180 Polyethylene 106-198 Polystyrene 90-150 Teflon 126-216

• Polymers

• CeramicsMagnesia (MgO) 13.5Alumina (Al2O3) 7.6Soda-lime glass 9Silica (cryst. SiO2) 0.4

• MetalsAluminum 23.6Steel 12 Tungsten 4.5 Gold 14.2

(10-6/C)at room T

Material

Polymers have larger

values because of weak secondary bonds

incr

eas

ing

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Thermal “Expansion”

Ex: A copper wire 15 m long is cooled from 40 to -9°C. How much change in length will it experience?

16.5 x 10 6 (C) 1

mm 12m 012.0

]C40)C9[()m 15)](C/1(10 x5.16[ 60

T

The linear coefficient of thermal expansion (CTE) of iron changes abruptly at temperatures where a phase transformation occurs.

Orton/Harrop Dilatometer

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©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

The relationship between the linear coefficient of thermal expansion and the melting temperature in metals. Higher melting point metals tend to expand to a lesser degree.

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The ability of a material to transport heat.

temperaturegradient

thermal conductivity (J/m-K-s)

heat flux

(J/m2-s)

• Atomic perspective: Atomic vibrations and free electrons in hotter regions transport energy to cooler regions.

T2 T2 > T1

T1

x1 x2heat flux

Thermal Conductivity

dx

dTkq

Fourier’s Law

Thermal Conductivity• Thermal conductivity, k, is the ability of a material

to conduct heat, and is an intensive property of that material.

• Thermal conductivity can be calculated from a number of measured quantities, but is normally defined as: the quantity of heat, Q, transmitted through a thickness L, in a direction normal to a surface with area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.

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20

Thermal Conductivity: Comparisonin

crea

sing

k

• PolymersPolypropylene 0.12Polyethylene 0.46-0.50 Polystyrene 0.13 Teflon 0.25

vibration/rotation of chain molecules

• CeramicsMagnesia (MgO) 38Alumina (Al2O3) 39 Soda-lime glass 1.7 Silica (cryst. SiO2) 1.4

atomic vibrations

• MetalsAluminum 247Steel 52 Tungsten 178 Gold 315

atomic vibrations and motion of free electrons

k (W/m-K)Energy Transfer

MechanismMaterial

• All-Clad Metalcrafters bond together different metals to capitalize on unique properties.

• Because the raw materials are critical to performance, All-Clad metallurgists specify the metal formulations down to the chemical composition and microstructure.

• Since quality always takes precedence over convenience, the metals are formulated for optimal cooking performance; not for ease of manufacturing.

• The “stay-cool” handle is cast from solid stainless steel, and is ergonomically-designed for comfort during long cooking sessions.

• Rivets are formed from high-yield-strength stainless steel, and treated to remove trace elements of iron that could otherwise cause corrosion.

Engineering Materials for Thermal Behavior

Easy-to-clean stainless steel interior will not react with food;Thick copper-core distributes heat evenly;Stainless steel exterior. Solid cast stainless steel handles; High quality white porcelain.          

Hand-hammered 1.2mm-gauge copper for superior heat conductivity and temperature control. Nonreactive tin interior is easy to clean. Heavy porcelain insert prohibits scorching of contents. Copper lid with bronze knob. Riveted bronze handles

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• Thermal stresses occur due to:

-- restrained thermal expansion/contraction

-- temperature gradients that lead to differential dimensional changes

Thermal Stresses (Ex 1)

TETTE f )( 0Thermal stress:

• A brass rod is stress-free at room temperature (20 °C).

• It is heated up, but prevented from expanding in length.

• At what temperature does the stress reach -172 MPa?

• E = 100 GPa for brass

• α = 20 x 10-6 / °C

/ (E α) = 20 °C - Tf

Tf = 20 °C - [-1.72 x 108 Pa / (1 x1011 Pa) (20 x 10-6 / °C)]

Tf = 20 °C + 86 °C

α = 106 °C

http://www.titanium.org/chinese/English/Technical%20Data/Alloy%20Characteristics/coefficientofexp.html

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• Occurs due to: nonuniform heating/cooling• Ex: Assume top thin layer is rapidly cooled from T1 to T2

Tension develops at surface

E(T1 T2)

Critical temperature difference

for fracture (set = f)

(T1 T2)fracture f

E

set equal

• Large TSR when is large

fk

E

Thermal Shock Resistance

Temperature difference thatcan be produced by cooling:

kTT

rate quench)( 21

rapid quench

resists contraction

tries to contract during cooling T2

T1

E

kTSR f )( stanceShock Resi Thermalrate) (quench fracturefor •

Thermal Cycling

• Satellites, spacecraft and all components must be able to withstand the rigors of a space environment while maintaining structural integrity throughout a mission that might last 10 years in low Earth orbit.

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NASA Space Environment and Experiments Branch

• Thermal Performance of an Annealed Pyrolytic Graphite Solar Collector

• A solar collector having the combined properties of high solar absorptance, low infrared emittance, and high thermal conductivity is needed for applications where solar energy is to be absorbed and transported for use in minisatellites.

• Electrical and Thermal Conductivity of Carbon Fiber-Polymer Composites Plates

• Composite thermal conductivity was measured using an optical heating technique and infrared scanning of the surface as well as being calculated from the rule of mixtures.

• Multi-Layer Thermal Control Coatings• Thermal control coatings on spacecraft will be increasingly

important as spacecraft grow smaller and more compact. New thermal control coatings will be needed to meet the demanding requirements of next generation spacecraft.

27http://www.nasa.gov/index.html

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Space Shuttle Atlantis

• Silica tiles (400-1260C):-- large scale application -- microstructure:

Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p. 1189.)

Thermal Protection System

reinf C-C (1650°C)

Re-entry T Distribution

silica tiles(400-1260°C)

nylon felt, silicon rubbercoating (400°C)

~90% porosity!Si fibersbonded to oneanother duringheat treatment.

100 m

Thermal Protection System (TPS)• The thermal protection system consists of various

materials applied externally to the outer structural skin of the orbiter to maintain the skin within acceptable temperatures, primarily during the entry phase of the mission.

• The orbiter's outer structural skin is constructed of aluminum and graphite epoxy.

• The materials are reusable for 100 missions with maintenance and perform in temperature ranges from minus 250 F (space) to entry temperatures that reach nearly 3,000 F.

• Reinforced carbon-carbon (RCC), used in the nose cap and wing leading edges. Used where reentry temperature exceeds 1260 °C (2300 °F).

• High-temperature reusable surface insulation (HRSI) tiles, used on the orbiter underside. Made of coated LI-900 Silica ceramics. Used where reentry temperature is below 1260 °C.

• Fibrous refractory composite insulation (FRCI) tiles, used to provide improved strength, durability, resistance to coating cracking and weight reduction.

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View of the Space Shuttle Discovery’s underside starboard wing and Thermal Protection System tiles

Who cares about thermal properties?

• Ryton® PPS (polyphenylene sulfide) is produced by Chevron Phillips Chemical as a high performance engineering resin known for dimensional stability and resistance to corrosive and high-temperature environments. With a thirty-plus year history, Ryton® PPS is recognized as the world’s premier product for demanding plastic components in automotive, electrical, appliance and industrial applications.

• Spec sheet for thermal properties: – Thermal Conductivity– Specific Heat– Differential Thermal Analysis– Coefficient of Linear Thermal Expansion– Thermal Degradation– NASA Outgassing Test

30http://www.cpchem.com/enu/docs_ryton/RytonThermalProperties.pdf

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• Thermoplastics: -- little cross linking -- ductile -- soften w/heating -- polyethylene polypropylene polycarbonate polystyrene

• Thermosets: -- significant cross linking (10 to 50% of repeat units) -- hard and brittle -- do not soften w/heating -- vulcanized rubber, epoxies, polyester resin, phenolic resin

Thermoplastics and Thermosets

Callister, Fig. 16.9

T

Molecular weight

Tg

Tmmobile liquid

viscous liquid

rubber

tough plastic

partially crystalline solid

crystalline solid

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Melting & Glass Transition Temps.

What factors affect Tm and Tg?

• Both Tm and Tg increase with increasing chain stiffness

• Chain stiffness increased by presence of

1. Bulky sidegroups

2. Polar groups or sidegroups

3. Chain double bonds and aromatic chain groups

• Regularity of repeat unit arrangements – affects Tm only

Melting The melting of a polymer crystal corresponds to the transformation

of a solid material: an ordered structure of aligned molecular chains becomes a viscous liquid where the structure is highly random.

This phenomenon occurs, upon heating, at the melting temperature, Tm.

There are several features peculiar to the melting of polymers that are not normally observed with metals and ceramics.

Melting of polymers takes place over a range of temperatures. The melting behavior depends on the crystallization temperature. The melting behavior is a function of the rate of melting; increasing

this rate results in an elevation of the melting temperature. Annealing also raises the Tm by decreasing vacancies and other imperfections.

The glass transition occurs in amorphous (or glassy) and semicrystalline polymers.

Caused by a reduction in motion of large segments of molecular chains with decreasing temperature.

Upon cooling, the glass transition corresponds to the gradual transformation from a liquid to a rubbery material, and finally to a rigid solid.

The temperature where polymer experiences the transition from rubbery to rigid is termed the glass transition temperature.

Aerogel Properties• Aerogel types: Carbon, Silica, Alumina• Other typical “extreme” properties of silica aerogel materials are: • Aerogels have the lowest thermal conductivity values of any solid • Aerogels are exceptional reflectors of audible sound, making

excellent barrier materials; aerogels have very low sound velocity through structure (~100 m/s)

• Aerogels can be exotic energy absorbers, showing capability to capture high velocity dust particles in space that would penetrate thick steel

• High internal surface areas (up to 1500 m2/g) • Ultra-low refractive index values for a solid (1.025), approaching that

for air • Ultra-low dielectric constants for a solid (can be < 1.1)

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http://www.aspenaerogels.com/features/morphology.htmlhttp://en.wikipedia.org/wiki/Aerogel

Silica Aerogels• One of the extraordinary properties that was discovered about first silica aerogels

was their very low thermal conductivity.

• In the1980s it was apparent that silica aerogels were an attractive alternative to traditional insulation due to their high insulating value and environment-friendly production methods.

• Aerogel materials are open cell, nanoporous materials that have a very high proportion of free void volume (typically >90%) compared to conventional solid materials.

• Silica aerogels prepared via sol-gel processing have some of the best thermal properties of any solid insulation material known.

• Excellent thermal insulation properties have also been reported in organic and carbon based aerogels as well as other inorganic metal oxides produced using sol-gel processing.

• The passage of thermal energy through an insulating material occurs through three mechanisms; solid conductivity, gaseous conductivity and radiative (infrared) transmission. The sum of these three components gives the total thermal conductivity of the material. For dense silica, solid conductivity is relatively high (a single-pane window transmits a large amount of thermal energy). However, silica aerogels possess a very small (~1-10%) fraction of solid silica.

Aerogel Titan

A 2.5 kg brick is supported on top of a piece of aerogel weighing only 2 grams

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39http://www.aerogel.com/features/pdf/atp_1.pdf

A comparison of thermal conductivity values at 1 atm of pressure and 20˚C for common materials along with some other related intensive properties (density, heat capacity and thermal diffusivity).

Invar• Invar (64 wt% Fe, 36 wt% Ni) is a nickel steel alloy notable for its uniquely low

coefficient of thermal expansion (CTE).

• When temperature varies 1° C, an Invar rod 10 km long expands in length by 0.8 - 2 cm depending on how it has been worked.

• A steel rod in the same conditions would vary 11 cm, a brass rod, 19 cm and an aluminum rod would increase in length by 25.5 cm.

• In recent years, NASA developed a particular kind of Invar, HP (High Purity) Invar 36. It has a much-improved coefficient of thermal expansion and structure stability than common Invar 36. A small quantity was used on the Cassini spacecraft camera.

• Process: Pure iron and nickel powders were weighed, mixed, pressed into a mold and sintered in controlled atmosphere. Half of the resulting product was extruded and half was hot hammered.The exceptional properties were attributed to the high purity of the alloy, especially to the very low carbon content (under 0.01%).

• Unfortunately, it cannot be purchased.

• [From the NASA Technical Support Package "Temporally and Thermally Stable Iron/Nickel Alloy" for the August 1995 issue of NASA Tech Briefs]

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Invar Elements Composition (% by Weight)Carbon 0.1 Max.

Manganese 0.3 to 0.6Phosphorus 0.025 Max.

Sulphur 0.025 Max.Silicon 0.35 Max.Nickel 35 to 37Cobalt 0.5 Max.

Chromium 0.5Molybdenum 0.5

Iron Remainder

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The thermal properties of materials include: • Heat capacity: -- energy required to increase a mole of material by a unit T -- energy is stored as atomic vibrations• Coefficient of thermal expansion: -- the size of a material changes with a change in temperature -- polymers have the largest values• Thermal conductivity: -- the ability of a material to transport heat -- metals have the largest values• Thermal shock resistance: -- the ability of a material to be rapidly cooled and not fracture

-- is proportional to

Summary

fk

E