Thermodynamic Summary Chapter 1

8/19/2019 Thermodynamic Summary Chapter 1

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T H E R M O D Y N A M I C S U M M A R Y O F C H A P T E R 1EDUCATION PHYSIC | Jl.Majapahit 62 Matara

TEMPERATURE AND THE !EROTH "A# OF THERMODYNAMICS#I"DAN HIDAYAT $E1%&1'&(1)


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1.1 MACROSCOPIC POINT OF VIEW

The study of any special branch of natural science starts with a separation of a restricted

region of space or a finite portion of matter from its surroundings by means of a closed surface

called the boundary. The region within the arbitrary boundary and on which the attention is

focused is called the system, and everything outside the system that has a direct bearing on the

system's

behavior is known as the surroundings, which could be another system. If no matter crosses the

boundary, then the system is closed; but if there is an exchange of matter between system and

surroundings, then the system is open.

There are, in general, two points of view that may be adopted: the macroscopic point of

view and the microscopic point of view. The macroscopic point of view considers variables or

characteristics of a system at approximately the human scale, or larger; whereas the microscopic

point of view considers variables or characteristics of a system at approximately the

molecular scale, or smaller.

or example, the contents in a cylinder of an automobile engine. ! chemical analysis

would show a mixture of hydrocarbons and air in cylinder. The contents can be describe by

specifying the "uantities of mass, composition, volume, pressure, and temperature. These

"uantities refer to the large#scale characteristics, or aggregate properties, of the system and

provide a macroscopic description. The "uantities are, therefore, called macroscopic

coordinates. The macroscopic coordinates, in general, have the following properties in common:

$. They involve no special assumptions concerning the structure of matter, fields, or radiation.

%. They are few in number needed to describe the system.

&. They are fundamental, as suggested more or less directly by our sensory perceptions.

. They can, in general, be directly measured.

1.2 MICROSCOPIC POINT OF VIEW

The microscopic point of view is the result of the tremendous progress of molecular,

atomic, and nuclear science during the past hundred years. rom this point of view, a system is


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considered to consist of an enormous number N of particles. The particles are assumed to interact

with one another by means of collisions or by forces caused by fields.

(umber of particles in each of the microscopic energy states )known as the populations

of the states* when e"uilibrium is reached. ! microscopic description of a system involves thefollowing properties:

$. !ssumptions are made concerning the structure of matter, fields, or radiation.

%. +any "uantities must be specified to describe the system.&. These "uantities specified are not usually suggested by our sensory perceptions, but rather

by our mathematical models.. They cannot be directly measured, but must be calculated.

1.3 MACROSCOPIC VS. MICROSCOPIC POINTS OF VIEW

oth points of view, applied to the same system, must lead to the same conclusion. The

few measurable macroscopic properties are as sure as our senses. They will remain unchanged as

long as our senses remain the same and are not deceived. The microscopic point of view,

however, goes much further than our senses and many direct experiments. It assumes the

structure of microscopic particles, their motion, their energy states, their interactions, etc., and

then calculates measurable "uantities. The microscopic point of view has changed several times,

and we can never be sure that the assumptions are -ustified until we have compared some

deduction made on the basis of these assumptions with a similar deduction based on the

experimentally proven macroscopic point of view.

1.4 SCOPE OF THERMODYNAMICS

In dealing with the mechanics of a rigid body, we adopt the macroscopic point of view in

that only the external aspects of the rigid body are considered. The position of its center of mass

is specified with reference to coordinate axes at a particular time. osition and time and a

combination of both, such as velocity, constitute some of the macroscopic "uantities used in

classical mechanics and are called mechanical coordinates.


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! macroscopic point of view is adopted, and emphasis is placed on those macroscopic

"uantities which have a bearing on the internal state of a system. +acroscopic "uantities,

including temperature, having a bearing on the internal state of a system are called

thermodynamic coordinates. /uch coordinates serve to determine the internal energy of a

system.

! system that may be described in terms of thermodynamic coordinates is called a

thermodynamic system.

1.5 THERMAL EQUILIBRIUM AND THE ZEROTH LAW

/ome thermodynamic systems composed of a number of homogeneous parts re"uire the

specification of two independent coordinates for each homogeneous part. In referring to any

unspecified system, we shall use the symbols X and Y for the pair of independent coordinates,

where the symbol X refers to a generali0ed force )for instance, the pressure of a gas* and Y refers

to a generali0ed displacement )for instance, the volume of a gas*.

! state of a system in which the coordinates X and Y have definite values that remain

constant so long as the external conditions are unchanged is called an equilibrium state.

1xperiment shows that the existence of an e"uilibrium state in one system depends on the

proximity of other systems and on the nature of the boundary or wall separating the different

systems. 2alls are said to be either adiabatic or diathermic in ideal cases. If a wall is adiabatic

3see ig. $#l)a*4, an e"uilibrium state for system A may coexist with any e"uilibrium state of

system B for all attainable values of the four "uantities, X, Y and X '

, Y '

- provided

only that the wall is able to withstand the stress associated with the difference between the two

sets of coordinates

If the two systems are separated by a diathermic wall 3see ig. $#l )b*4, the values of X, Y

and X '

, Y '

will change spontaneously until an e"uilibrium state of the combined system is

attained. The two systems are then said to be in thermal equilibrium with each other. Thermal

equilibrium is the state achieed by two !or more" systems, characteri#ed by restricted alues o$


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the coordinates o$ the

systems, a$ter they hae

been in communication

with each other through

a diathermic wall.

Imagine two systems A and B, separated from each other by an adiabatic wall but each in

contact simultaneously with a third system % through diathermic walls, the whole assembly

being surrounded by an adiabatic wall as shown in ig. l#%)a*. 1xperiment shows that the two

systems will come to thermal e"uilibrium with the third system. (o further change will occur if

the

adiabatic wall separating A and B is then replaced by a diathermic wall, as well as if the

diathermic wall separating % from both A and B is also replaced by an adiabatic wall 3ig. $#

%)b*4.

These experimental facts may then be stated concisely in the following transitive relation:

Two systems in thermal equilibrium with a third are in thermal equilibrium with each other. !s

suggested by 5alph owler, this postulate of transitive thermal e"uilibrium has been numbered


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the #eroth law o$ thermodynamics, which establishes the basis for the concept of temperature

and for the use of thermometers.


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1.6 CONCEPT OF TEMPERATURE

! scientific understanding of the concept of temperature builds upon thermal e"uilibrium,

established in the 0eroth law of thermodynamics. 6onsider a system A in the state X 1 , Y 1

in thermal e"uilibrium with

another system B in the

state X 1'

, Y 1'

. If

system A is removed and its

state changed,

there will be found a

second state X 2 , Y 2

that is in thermal

e"uilibrium with the original state X 1'

, Y 1'

of system B. 1xperiment shows that there exists

a whole set of states # X 1 , Y 1 ; X 2 , Y 2 ; X 3 , Y 3 - any one of which is in

thermal e"uilibrium with this same state X 1'

, Y 1'

of system B, and all of which, by the

0eroth law, are in thermal e"uilibrium with one another. 2e shall suppose that all such states,

when plotted on an X-Y diagram, lie on a curve such as I in ig. $#&, which we shall call an

isotherm. An isotherm is the locus o$ all points representing states in which a system is in

thermal equilibrium with one state o$ another system.

/imilarly, with regard to system B, we find a set of states # X 1'

, Y 1'

; X 2'

, Y 2'

;

X 3'

, Y 3'

- all of which are in thermal e"uilibrium with one state ) X 1 , Y 1 * of system A,

and, therefore, in thermal e"uilibrium with one another. These states are plotted on the X 1'

,

Y 1'

diagram of ig. $#& and lie on the isotherm I'. rom the 0eroth law, it follows that all the

states on isotherm I of system A are


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in thermal e"uilibrium with all the states on isotherm I '

of system B. 2e shall call curves I

and I '

corresponding isotherms of the two systems.

To determine whether or not two beakers of water are in e"uilibrium, it is not necessary

to bring them into contact by means of a diathermic wall and see if their properties change with

time. 5ather, an unmarked glass capillary tube filled with mercury )system A" is inserted into the

first beaker )system B" and, shortly, some property of this device, such as the height of the

mercury

column, comes to rest. /uch a device is a thermoscope, which indicates only e"uality of

temperature for the corresponding isotherms of the systems.

1.7 THERMOMETERS AND MEASUREMENT OF TEMPERATURE

To establish an empirical

temperature scale, we select

some system with

coordinates X and Y as a

standard, which we call a

thermometer. The simplest

procedure is to choose any

convenient path in the X - Y

plane, such as that

shown in ig. $# by the

dashed line Y 7 Y 1 ,

which intersects the isotherms at points each of which has the same 8#coordinate but a different

9#coordinate. The temperature associated with each isotherm is then taken to be a convenient

function of the X at this intersection point. The coordinate X is called the thermometric property,

and the form of the thermometric $unction &!X" determines the empirical temperature scale.


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et X stand for any one of the thermometric properties listed in Table $.$, and let us

decide arbitrarily to define the temperature scale so that the empirical temperature is directly

proportional to X. Thus, the temperature common to the thermometer and to all systems in

thermal equilibrium with it can be given by the thermometric function,

&!X" = ax )constant ϒ) )$. $*

where a is an arbitrary constant. (otice that as the coordinate X approaches 0ero, the temperature

also approaches 0ero,

2hen the thermometer is placed in contact with an arbitrarily chosen standard system in

a reproducible state; such a state of an arbitrarily chosen standard system is called a $i'ed point,

that is, fixed temperature. The fixed point provides a reference temperature for the

determination of temperature scales.

efore $> ?degrees? )of hotness*, abbreviated as $>>@6.

In $


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temperature. The temperature of the triple point of water, which can be very accurately and

reproducibly measured, was assigned the value %B&.$C kelvin, corresponding to >.>$ @6, in order

to maintain the magnitude of a unit of temperature. 2e can now solve 1". )$.$* for the

coefficient a:

a=273.16 K

X TP

$1.2)

2here the subscript T( identifies the property value X TP explicitly with the triple#point

temperature. The temperature of the triple point of water is the standard $i'ed point of

thermometry. To achieve the triple point, one distills water of the highest purity and of

substantially the same isotopic composition of ocean water into a vessel depicted schematically

in ig. $#=. 2hen all air has been removed, the vessel is sealed off. 2ith the aid of a free0ing

mixture in the inner well, a layer of ice is formed around the well. 2hen the free0ing mixture

is replaced by a thermometer bulb, a thin layer of ice is melted nearby. /o long as the solid,

li"uid, and vapor phases coexist in e"uilibrium, the system is at the triple point.

1. COMPARISON OF THERMOMETERS


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!pplying the principles outlined in the preceding paragraphs to the first three thermometers

listed in Table $.$, we have three different ways of measuring temperature. Thus, for a gas at

constant volume,

&!(" 7 )*+.l P PTP

)constant "; )$.&*

for a platinum wire resistor,

&! R'

" 7 )*+.l R

'

R'

TP;

and for a thermocouple,

&! "Ɛ 7 )*+.lƐ

ƐTP

;

/uch a comparison is shown in Table $.%, where the constant#volume gas thermometer is used at

high pressure and low pressure. The letters ( stand for the normal boiling point, by which the

word normal specifies that the temperature at which a li"uid boils occurs at standard atmospheric

pressure )$>$,&%= a or $.B lbDi n2

*, /imilarly, the letters (+ stand for the normal melting

point,


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(/ for the normal sublimation point, and T for the triple point, the temperature at which the

solid, li"uid, and vapor coexist in thermal e"uilibrium. The numerical values are not meant to be

exact, and %B&.$C has been written simply %B&.

1.! "AS THERMOMETER

! simplified schematic diagram of a constant#volume gas thermometer is shown in ig. $#C. The

gas is contained in the glass bulb B , which communicates with the mercury column / through a

capillary

.

The volume of the gas is kept constant by ad-usting the height of the mercury column /

until the mercury level -ust touches the tip of a small pointer )indicial point* in the space above

/, known as the dead space or nuisance olume. The mercury column + is ad-usted by raising

or lowering the reservoir . The pressure in the system e"uals atmospheric pressure plus the

difference in height h between them two mercury columns / and M '

and is measured twice:

when the bulb is surrounded by the system whose temperature is to be measured, and when it is

surrounded by water at the triple point. The various values of the pressure must be corrected to

take account of many sources of error, such as:


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$. The gas present in the dead space )and in any other nuisance volumes* is at a temperature

different from that in the bulb.%. The gas in the capillary connecting the bulb with the manometer has a temperature gradient;

that is, it is not at a uniform temperature.

&. The bulb, capillary, and nuisance volumes undergo changes of volume when the temperatureand pressure change.

. ! pressure gradient exists in the capillary when the diameter of the capillary is comparable

to the mean free path of the gas particles.

=. /ome gas is adsorbed on the walls of the bulb and capillary; the lower the temperature, the

greater the adsorption.6. There are effects due to temperature and compressibility of the mercury in

the manometer.

Improvements and alternative ways of measuring pressure have been incorporated into thedesign of gas thermometers, so these errors can be estimated and eliminated from the data. !s a

result, the behavior of real gases approaches the behavior of the ideal gas in limiting conditions.

1.1# IDEAL$"AS TEMPERATURE

The theoretical basis for gas thermometry became the well#understood relationship between

pressure, volume, and temperature embodied in the ideal-gas law, namely,

PV * nRT, $1.')

where ( is the pressure of the system of gas, is the volume of gas, n is the number of moles of

gas, and 0 is the molar gas constant. The temperature T is the theoretical thermodynamic

temperature. In this section, we show the experiment that yields reproducible and accurate

empirical temperatures B. The ideal#gas temperature is found using a constant#volume gas

thermometer. !pplying 1". )$.* initially to the gas at the assigned temperature of %B&.$C A and

then to the gas at the unknown empirical temperature, one obtains the proportion

P

PTP

= θ

273.16 K ,


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or 7 %B&.$C A P

PTP

$+,-ta-t V).

$1.()

6onsider measuring the ideal-gas temperature at the normal boiling point )(* of water

)the steam point*. !n amount of gas is introduced into the bulb of a constant#volume gas

thermometer, and one measures PTP when the bulb of the constant#volume thermometer is

inserted in the triple#point cell shown in ig. $#=. /uppose that PTP is e"ual to $%> ka.

Aeeping the volume

constant, carry out the following procedures:

1. /urround the bulb with steam at standard atmospheric pressure, measure the gas pressure

P NBP , and calculate the empirical temperature using 1". )$.C*,

/ $ P NBP ) * %B&.$C A P

NBP

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2. 5emove some of the gas so that PTP has a smaller measured value, say, C> ka. +easure

the new value of P NBP and calculate a new value,

/ $ P NBP ) * %B&.$C A P NBP

60

&. 6ontinue reducing the amount of gas in the bulb so that PTP and P NBP have smaller

and smaller values0 PTP having values of, say, > ka, %> ka, etc. !t each value of

PTP , calculate the corresponding /$ P NBP )·

. lot /( P NBP ) against PTP and extrapolate the resulting curve to the axis where PTP

* &. 5ead from the graph,lim

PTP→0

θ( P NBP)

The results of a series of tests of this sort are plotted in ig. $#B for three different gases

in order to measure !(" for the normal boiling point of water. The graph conveys the

information that, although the readings of a constant volume gas thermometer depend upon the


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nature of the gas at ordinary values of P NBP , all gases indicate the same temperature as

PTP is lowered and made to approach #ero.

Therefore, we define the ideal-gas temperature T by the e"uation

T * 2.163 lim PTP→0

P

PTP

$+,-ta-t V). $1.6)

1.11 CELSIUS TEMPERATURE SCALE

The 6elsius temperature scale, named after the /wedish astronomer !nders 6elsius, was the

international temperature scale prior to the introduction of the Aelvin scale in $.>$ @6 above the ice point of water, that is %B&.$C A. The relationship

between the 6elsius scale and the Aelvin scale is simply

/$4C) * T (K) - 2.1(. $1.)


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or example, the 6elsius temperature θ NBP at which water boils at standard atmospheric

pressure is

θ NBP * T NBP - 2.1(0

and reading T NBP from ig. $#B,

θ NBP−373.124−273.15−99.974 ° C

1.12 PLATINUM RESISTANCE THERMOMETRY

The platinum resistance thermometer may be used for very accurate work within the

range $&.E>&& to $%&.


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Fptical pyrometry, radiation pyrometry, infrared pyrometry, and spectral or total#radiation

pyrometry are some of the methods of thermometry based on the measurement of thermal

radiation, or so#called blac4body radiation.

5adiation thermometers called pyrometers were developed for measuring hightemperatures )greater than approximately $$>> @6*, and they have the advantage that they are

noncontact thermometers. Fptical pyrometers measure temperatures of ob-ects by comparing the

visible radiation from the hot ob-ects over a narrow wavelength band with the radiation from a

standard, preferably using a photoelectric detector for measurements rather than the human eye.

1.14 VAPOR PRESSURE THERMOMETR

/aturation vapor pressure thermometry is commonly used for the measurement of temperature in

the range between >.& and =.% A, because of the sensitivity and convenience of this type

of measurement. The thermometric substance is the vapor in e"uilibrium with the li"uid of either

of the two isotopes of helium: He❑3

or He❑4

. Gelium vapor pressure is the

thermometric

parameter, because it depends only on a physical property of a pure element and can be

reproduced at any time, it re"uires no interpolation device, and it is relatively easy to measure

with sufficient precision over much of the temperature range.

1.15 THERMOCOUPLE

! schematic diagram of a thermocouple is shown in ig. $#E, where the temperature to be

measured is located at the test -unction. The thermal electromotive force )emf* is generated at the

point where wire A and wire B are -oined. The two thermocouple wires are connected to copper

wires located at the reference -unction, which is maintained at the temperature of melting ice.


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! thermocouple is

calibrated by measuring the

thermal emf at the test

-unction at various known

temperatures, the reference

-unction being kept at > @6.

The results of such

measurements on most

thermocouples can usually

be represented by a cubic

e"uation, as follows:

Ɛ−c0−c10−c202−c30

3

where Ɛ is the thermal emf, and the constantsc0 ,

c1 ,

c2 . and

c3 are different for each

thermocouple. 2ithin a restricted range of temperature, a "uadratic e"uation is often sufficient.

The temperature range of a thermocouple depends upon the materials of which it is composed.

The type A thermocouple, made of a chromel wire )H (i and $>H 6r* and an alumel wire

) to $&B%@6.

1.16 INTERNATIONAL TEMPERATURE SCALE OF 1!!# %ITS$!#&

The International 6ommittee of 2eights and +easures is concerned with two temperature scales:

the first is the theoretical thermodynamic scale; the second is, at any given time, the current

practical temperature scale.


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The International Temperature /cale of $.C= A. elow this temperature, the scale is

undefined in terms of a standardi0ed thermometer, but research continues in order to select a

reference thermometer from competing instruments. arious intervals of temperature on IT/#

and secondary thermometers are established, as follows:

$. 5rom 6.7 to 7.6 . etween >.C= and &.% A, the IT/# is defined by the vapor pressure#

temperature relations of He❑3

, and between $.%= and %.$BCE A )the J#point* and between

%.$BCE and =.> A by the vapor pressure#temperature relations of He❑4

.

%. 5rom +.6 to )8.779 . etween &.> and %.==C$ A, the IT/# is defined by the He❑3

or

He❑4

constant#volume gas thermometer.

&. 5rom 9+.:6++ to 9)+8.+ . etween $&.E>&& and $%&.


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specified fixed points given in Table $.& and by reference functions and deviation functions

of resistance ratios between the fixed points. 1leven subranges have been established to

accommodate a variety of necessary measurements.

. Aboe 9)+8.+ . !t temperatures above $%&.


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Thermodynamic Summary Chapter 1

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