assinment of i.math

8/13/2019 Assinment of i.math

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THERMODYNAMIC PROPERTIES

1. TEMPERATUREA temperature is a numerical measure of hot or cold. Its measurement is by detection of heat

radiation or particle velocity or kinetic energy, or by the bulk behavior of a thermometric

material. It may becalibrated in any of various temperature scales,Celsius, Fahrenheit, Kelvin,

etc. The fundamental physical definition of temperature is provided bythermodynamics.

A temperature is a numerical measure of hot or cold. Its measurement is by detection of heat

radiation or particle velocity or kinetic energy, or by the bulk behavior of a thermometric

material. It may becalibrated in any of various temperature scales,Celsius, Fahrenheit, Kelvin,

etc. The fundamental physical definition of temperature is provided bythermodynamics.

Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of

incremental units or degrees on the scale.

TheCelsius scale (C) is used for common temperature measurements in most of the world. It is

an empirical scale. It developed by a historical progress, which led to its zero point 0C being

defined by the freezing point of water, with additional degrees defined so that 100C was the

boiling point of water, both at sea-level atmospheric pressure. Because of the 100 degree

interval, it is called a centigrade scale. Since the standardization of the kelvin in the International

System of Units, it has subsequently been redefined in terms of the equivalent fixing points on

the Kelvin scale, and so that a temperature increment of one degree Celsius is the same as an

increment of one degree kelvin, though they differ by an additive offset of 273.15.

The United States commonly uses theFahrenheit scale, on which water freezes at 32 F and boils

at 212 F at sea-level atmospheric pressure.

Temperature is a measure of aquality of a state of a material[30]

The quality may be regarded as

a more abstract entity than any particular temperature scale that measures it, and is called hotness
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by some writers. The quality of hotness refers to the state of material only in a particular locality,

and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness

varies from place to place. It is not necessarily the case that a material in a particular place is in a

state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or

temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid

temperature scale has its own one-to-one map into the hotness manifold.[31][32]
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2. PRESUREPressure is a measure of the force exerted per unit area on the boundaries of a substance (or

system). It is caused by the collisions of the molecules of the substance with the boundaries of

the system. As molecules hit the walls, they exert forces that try to push the walls outward. The

forces resulting from all of these collisions cause the pressure exerted by a system on its

surroundings. Pressure is frequently measured in units of lbf/in2 (psi).

Pressure is force per unit area applied in a direction perpendicular to the surface of an object.

Pressure is measured in any unit of force divided by any unit of area. TheSI unit of pressure is

the newton per square metre, which is called the Pascal (Pa) after the seventeenth-century

philosopher and scientistBlaise Pascal.A pressure of 1 Pa is small; it approximately equals the

pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in

kilopascals (1 kPa = 1000 Pa).

Mathematically:

where:

is the pressure
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is thenormal force,

is the area of the surface on contact.

Pressure is ascalar quantity. It relates the vector surface element (a vector normal to the surface)

with the normal force acting on it. The pressure is the scalarproportionality constant that relates

the two normal vectors:

The SI unit for pressure is the Pascal (Pa), equal to one newton per square metre (N/m2 or

kgm1

s2

). This special name for the unit was added in 1971; before that, pressure in SI was

expressed simply as N/m2.
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3. DENSITYThe density of a substance is the total mass (m) of that substance divided by the total volume(V) occupied by that substance (mass per unit volume). It has units of pound-mass per cubic feet

(lbm/ft3). The density of a substance is the reciprocal of its specific volume (n).

The density, or more precisely, the volumetric mass density, of a substance is itsmassper unit

volume. The symbol most often used for density is (the lower case Greek letter rho).

Mathematically, density is defined as mass divided by volume:

where is the density, m is the mass, and V is the volume. In some cases (for instance, in the

United States oil and gas industry), density is loosely defined as its weight per unit volume

although this is scientifically inaccuratethis quantity is more properly calledspecific weight.

density

Common symbol(s):

SI unit: kg/m3
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HISTORY

In a well-known but probably apocryphal tale, Archimedes was given the task of determiningwhetherKing Hiero'sgoldsmith was embezzlinggold during the manufacture of a goldenwreath

dedicated to the gods and replacing it with another, cheaper alloy. Archimedes knew that the

irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily

and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to

have taken an immersion bath and observed from the rise of the water upon entering that he

could calculate the volume of the gold wreath through thedisplacement of the water. Upon this

discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!"

(! Greek "I have found it"). As a result, the term "eureka"entered common parlance and

is used today to indicate a moment of enlightenment.

The story first appeared in written form inVitruvius'books of architecture,two centuries after it

supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other

things that the method would have required precise measurements that would have been difficult

to make at the time.

From the equation for density (= m/ V), mass density has units of mass divided by volume. As

there are many units of mass and volume covering many different magnitudes there are a large

number of units for mass density in use. TheSI unit ofkilogrampercubic metre (kg/m3) and the

cgs unit of gramper cubic centimetre (g/cm3) are probably the most commonly used units for

density. (The cubic centimeter can be alternately called a milliliter or a cc.) 1,000 kg/m3equals

one g/cm3. In industry, other larger or smaller units of mass and or volume are often more

practical andUS customary units may be used. See below for a list of some of the most common

units of density.

Measurement of density

The density at all points of a homogeneous object equals its total mass divided by its total

volume. The mass is normally measured with a scale or balance;the volume may be measured
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directly (from the geometry of the object) or by the displacement of a fluid. To determine the

density of a liquid or a gas, ahydrometer or daisy meter may be used, respectively. Similarly,

hydrostatic weighing uses the displacement of water due to a submerged object to determine the

density of the object.

If the body is not homogeneous, then its density varies between different regions of the object. In

that case the density around any given location is determined by calculating the density of a

small volume around that location. In the limit of an infinitesimal volume the density of an

inhomogeneous object at a point becomes: (r) = dm/dV, where dV is an elementary volume at

position r. The mass of the body then can be expressed as

In contrast, the density of gases is strongly affected by pressure. The density of anideal gas is
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4. INTERNAL ENERGYInternal energy is defined as the energy associated with the random, disordered motion of

molecules. It is separated in scale from the macroscopic ordered energy associated with moving

objects; it refers to the invisible microscopic energy on the atomic and molecular scale. For

example, a room temperature glass of water sitting on a table has no apparent energy, either

potential orkinetic .But on the microscopic scale it is a seething mass of high speed molecules

traveling at hundreds of meters per second. If the water were tossed across the room, this

microscopic energy would not necessarily be changed when we superimpose an ordered large

scale motion on the water as a whole.

Uis the most common symbol used for internal energy.

The internal energy is the total energy contained by a thermodynamic system.It is the energy

needed to create the system but excludes the energy to displace the system's surroundings, any

energy associated with a move as a whole, or due to external force fields. Internal energy has two

major components,kinetic energy andpotential energy.The kinetic energy is due to the motion

of the system's particles (translations,rotations,vibrations), and the potential energy is associated

with the static rest mass energy of the constituents of matter, static electric energy of atoms

within molecules or crystals,and the static energy of chemical bonds.The internal energy of a

system can be changed by heating the system or by doing work on it;[1]

the first law of

thermodynamics states that the increase in internal energy is equal to the total heat added and

work done by the surroundings. If the system is isolated from its surroundings, its internal energy
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cannot change. For practical considerations in thermodynamics and engineering it is rarely

necessary or convenient to consider all energies belonging to the total intrinsic energy of a

sample system, such as the energy given by the equivalence of mass. Typically, descriptions only

include components relevant to the system under study. Thermodynamics is chiefly concerned

only with changes in the internal energy.

The internal energy is astate function of asystem,because its value depends only on the current

state of the system and not on the path taken or process undergone to arrive at this state. It is an

extensive quantity. The SI unit of energy is the joule (J). Some authors use a corresponding

intensive thermodynamic property called specific internal energy which is internal energy per

unit of mass (kilogram)of the system in question. The SI unit of specific internal energy is J/kg.

If intensive internal energy is expressed relative to units ofamount of substance (mol), then it isreferred to as molar internal energy and the unit is J/mol.

Internal Energy Example

When the sample of water and copper are both heated by 1c, the addition to the kinetic energy is

the same, since that is what temperature measures. But to achieve this increase for water, a much

larger proportional energy must be added to the potential energy portion of the internal energy.
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So the total energy required to increase the temperature of the water is much larger, i.e., its

specific heat is much larger.

5. ENTHALPYEnthalpy is a measure of the total energy of a thermodynamic system.It includes the

system'sinternal energy orthermodynamic potential (astate function), as well as itsvolume and

pressure (the energy required to "make room for it" by displacing its environment,which is an

extensive quantity). The unit of measurement for enthalpy in theInternational System of Units

(SI) is the joule, but other historical, conventional units are still in use, such as the British

thermal unit and thecalorie.

Formal definition

The enthalpy of a homogeneous system is defined as:

Where

His the enthalpy of the system

Uis theinternal energy of the system

pis thepressure of the system

Vis thevolume of the system.

The enthalpy is anextensive property.This means that, for homogeneous systems, the enthalpy

is proportional to the size of the system. It is convenient to introduce the specific enthalpy h

=H/mwhere mis the mass of the system, or the molar enthalpy Hm= H/n, where nis the number

of moles (h and Hm are intensive properties). For inhomogeneous systems the enthalpy is the

sum of the enthalpies of the composing subsystems
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where the label krefers to the various subsystems. In case of continuously varying p, T, and/or

composition the summation becomes an integral:

where is the density.

The enthalpy H(S,p) of homogeneous systems can be derived as a characteristic function of the

entropy Sand the pressure pas follows: we start from thefirst law of thermodynamics for closed

systems for an infinitesimal process

Here, Q is a small amount of heat added to the system and W a small amount of work

performed by the system. In a homogeneous system only reversible processes can take place so

the second law of thermodynamics gives Q = TdS with T the absolute temperature of the

system. Furthermore, if only pV work is done, W= pdV. As a result

Adding d(pV) to both sides of this expression gives

or

So
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Applications

In thermodynamics, one can calculate enthalpy by determining the requirements for creating a

system from "nothingness"; the mechanical work required, pV, differs based upon the constancy

of conditions present at the creation of thethermodynamic system.

Internal energy,U, must be supplied to remove particles from a surrounding in order to allow

space for the creation of a system, providing that environmental variables, such as pressure (p)

remain constant. This internal energy also includes the energy required for activation and the

breaking of bonded compounds into gaseous species.

This process is calculated within enthalpy calculations as U + pV, to label the amount of energy

or work required to "set aside space for" and "create" the system; describing the work done by

both the reaction or formation of systems, and the surroundings. For systems at constant

pressure, the change in enthalpy is the heat received by the system.

Therefore, the change in enthalpy can be devised or represented without the need for

compressive or expansive mechanics; for a simple system, with a constant number of particles,

the difference in enthalpy is the maximum amount of thermal energy derivable from a

thermodynamic process in which the pressure is held constant.

The term pV is the work required to displace the surrounding atmosphere in order to vacate the

space to be occupied by the system.

Heat of reaction

The total enthalpy of a system cannot be measured directly; the enthalpy change of a system is

measured instead. Enthalpy change is defined by the following equation:

where

is the "enthalpy change"
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is the final enthalpy of the system, expressed in joules. In a chemical reaction, is the

enthalpy of the products.

is the initial enthalpy of the system, expressed in joules. In a chemical reaction, is the

enthalpy of the reactants.

For an exothermic reaction at constant pressure, the system's change in enthalpy equals the

energy released in the reaction, including the energy retained in the system and lost through

expansion against its surroundings. In a similar manner, for an endothermic reaction, the

system's change in enthalpy is equal to the energy absorbed in the reaction, including the energy

lost by the system and gained from compression from its surroundings. A relatively easy way to

determine whether or not a reaction is exothermic or endothermic is to determine the sign of H.If H is positive, the reaction is endothermic, that is heat is absorbed by the system due to the

products of the reaction having a greater enthalpy than the reactants. On the other hand if H is

negative, the reaction is exothermic, that is the overall decrease in enthalpy is achieved by the

generation of heat.

Although enthalpy is commonly used in engineering and science, it is impossible to measure

directly, as enthalpy has no datum (reference point). Therefore enthalpy can only accurately be

used in aclosed system.However, few real-world applications exist in closed isolation, and it is

for this reason that two or more closed systems cannot correctly be compared using enthalpy as a

basis.

Specific enthalpy

As noted before, the specific enthalpy of a uniform system is defined as h = H/m where m is the

mass of the system. TheSI unit for specific enthalpy is joule per kilogram. It can be expressed in

other specific quantities by h = u + pv, where u is the specificinternal energy,p is the pressure,

and v is specific volume, which is equal to 1/, where is the density.
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6. ENTROPYEntropy is a measure of the number of specific ways in which a system may be arranged,

often taken to be a measure of disorder, or a measure of progressing towards

thermodynamic equilibrium. The entropy of an isolated system never decreases, because

isolated systems spontaneously evolve towards thermodynamic equilibrium, which is the

state of maximum entropy.

Entropy was originally defined for athermodynamically reversible process as

where the entropy (S) is found from the uniform thermodynamic temperature (T) of a closed

system dividing an incremental reversible transfer of heat into that system (dQ). The above

definition is sometimes called the macroscopic definition of entropy because it can be used

without regard to any microscopic picture of the contents of a system. In thermodynamics,

entropy has been found to be more generally useful and it has several other formulations.

Entropy was discovered when it was noticed to be a quantity that behaves as a function of state.

Entropy is anextensive property,but it is often given as anintensive property of specific entropy

as entropy per unit mass or entropy per mole.
http://en.wikipedia.org/wiki/Reversible_process_%28thermodynamics%29http://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Closed_systemhttp://en.wikipedia.org/wiki/Closed_systemhttp://en.wikipedia.org/wiki/Function_of_statehttp://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Extensive_propertieshttp://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Intensive_propertieshttp://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Intensive_propertieshttp://en.wikipedia.org/wiki/Intensive_and_extensive_properties#Extensive_propertieshttp://en.wikipedia.org/wiki/Function_of_statehttp://en.wikipedia.org/wiki/Closed_systemhttp://en.wikipedia.org/wiki/Closed_systemhttp://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Reversible_process_%28thermodynamics%29


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7. COFFICIENT OF VISCOSITY

The viscosity of afluid is a measure of its resistance to gradual deformation byshear stress or

tensile stress. For liquids, it corresponds to the informal notion of "thickness". For example,

honey has a higher viscosity thanwater.

Viscosity is due tofrictionbetween neighboring parcels of the fluid that are moving at different

velocities.When fluid is forced through a tube, the fluid generally moves faster near the axis and

very slowly near the walls, therefore somestress (such as apressure difference between the two

ends of the tube) is needed to overcome the friction between layers and keep the fluid moving.

For the same velocity pattern, the stress required is proportional to the fluid's viscosity. A liquid'sviscosity depends on the size and shape of its particles and the attractions between the particles.

Shear viscosity

Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries

causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity.
http://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Drag_%28physics%29http://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Stress_%28physics%29http://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/File:Laminar_shear.svghttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Stress_%28physics%29http://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Shear_stresshttp://en.wikipedia.org/wiki/Drag_%28physics%29http://en.wikipedia.org/wiki/Fluid


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In a general parallel flow (such as could occur in a straight pipe), the shear stress is proportional

to the gradient of the velocity The shear viscosity of a fluid expresses its resistance to shearing

flows, where adjacent layers move parallel to each other with different speeds. It can be defined

through the idealized situation known as a Couette flow, where a layer of fluid is trapped

between two horizontal plates, one fixed and one moving horizontally at constant speed . (The

plates are assumed to be very large, so that one need not consider what happens near their

edges.)

The magnitude of this force is found to be proportional to the speed and the area of each

plate, and inversely proportional to their separation . That is,
http://en.wikipedia.org/wiki/Couette_flowhttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/File:Laminar_shear_flow.svghttp://en.wikipedia.org/wiki/Couette_flow


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The measure of the viscosity of a fluid, equal to theforceper unit area required to maintain a

difference of velocity of one unit distance per unit time between two parallel planes in the fluid

that lie in the direction of flow and are separated by one unit distance: usually expressed in poise

or centipoise.
http://dictionary.reference.com/browse/forcehttp://dictionary.reference.com/browse/force


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8. THERMAL CONDUCTIVITYInphysics,thermal conductivity (often denoted k, , or ) is theproperty of a material toconduct

heat.It is evaluated primarily in terms ofFourier's Law forheat conduction.

Heat transfer occurs at a higher rate across materials of high thermal conductivity than across

materials of low thermal conductivity. Correspondingly materials of high thermal conductivity

are widely used in heat sink applications and materials of low thermal conductivity are used as

thermal insulation.Thermal conductivity of materials is temperature dependent. The reciprocal

of thermal conductivity is called thermal resistivity.

Definitions

The reciprocal of thermal conductivity is thermal resistivity, usually expressed in kelvin-meters

per watt (KmW1

). For a given thickness of a material, that particular construction's thermal

resistance and the reciprocal property, thermal conductance, can be calculated. Unfortunately,

there are differing definitions for these terms.

Units of thermal conductivity

In SI units, thermal conductivity is measured in watts per meter kelvin (W/ (mK)). The

dimension of thermal conductivity is M1L

1T

3

1. These variables are (M) mass, (L) length, (T)

time, and () temperature. In Imperial units, thermal conductivity is measured in BTU/

(hrftF).

Other units which are closely related to the thermal conductivity are in common use in the

construction and textile industries. The construction industry makes use of units such as theR-

value (resistance) and theU-value (conductivity). Although related to the thermal conductivity of

a material used in an insulation product, R and U-values are dependent on the thickness of theproduct.

Likewise the textile industry has several units including the tog and the Klo which express

thermal resistance of a material in a way analogous to the R-values used in the construction

industry.
http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/List_of_materials_propertieshttp://en.wikipedia.org/wiki/Heat_conductionhttp://en.wikipedia.org/wiki/Heathttp://en.wikipedia.org/wiki/Heat_conduction#Fourier.27s_lawhttp://en.wikipedia.org/wiki/Heat_conductionhttp://en.wikipedia.org/wiki/Heat_sinkhttp://en.wikipedia.org/wiki/Thermal_insulationhttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/Watthttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Imperial_unitshttp://en.wikipedia.org/wiki/British_thermal_unithttp://en.wikipedia.org/wiki/Hourhttp://en.wikipedia.org/wiki/Foot_%28unit%29http://en.wikipedia.org/wiki/Fahrenheithttp://en.wikipedia.org/wiki/Fahrenheithttp://en.wikipedia.org/wiki/R-value_%28insulation%29http://en.wikipedia.org/wiki/R-value_%28insulation%29http://en.wikipedia.org/wiki/R-value_%28insulation%29#U-factorhttp://en.wikipedia.org/wiki/Tog_%28unit%29http://en.wikipedia.org/wiki/Thermal_Comforthttp://en.wikipedia.org/wiki/Thermal_Comforthttp://en.wikipedia.org/wiki/Tog_%28unit%29http://en.wikipedia.org/wiki/R-value_%28insulation%29#U-factorhttp://en.wikipedia.org/wiki/R-value_%28insulation%29http://en.wikipedia.org/wiki/R-value_%28insulation%29http://en.wikipedia.org/wiki/Fahrenheithttp://en.wikipedia.org/wiki/Foot_%28unit%29http://en.wikipedia.org/wiki/Hourhttp://en.wikipedia.org/wiki/British_thermal_unithttp://en.wikipedia.org/wiki/Imperial_unitshttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Watthttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/Thermal_insulationhttp://en.wikipedia.org/wiki/Heat_sinkhttp://en.wikipedia.org/wiki/Heat_conductionhttp://en.wikipedia.org/wiki/Heat_conduction#Fourier.27s_lawhttp://en.wikipedia.org/wiki/Heathttp://en.wikipedia.org/wiki/Heat_conductionhttp://en.wikipedia.org/wiki/List_of_materials_propertieshttp://en.wikipedia.org/wiki/Physics


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Measurement

There are a number of ways to measure thermal conductivity. Each of these is suitable for a

limited range of materials, depending on the thermal properties and the medium temperature.

There is a distinction between steady-state and transient techniques.

In general, steady-state techniques are useful when the temperature of the material does not

change with time. This makes the signal analysis straightforward (steady state implies constant

signals). The disadvantage is that a well-engineered experimental setup is usually needed. The

Divided Bar (various types) is the most common device used for consolidated rock solids.

assinment of i.math

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