Thermodynamics – chapter - 1- 1 References 1// An introduction to thermodynamics, the kinetic theory of gases, and statistical mechanics. By/ Francis Weston Sears. ( 1953 ) 2// Thermodynamics, kinetic theory, and statistical thermodynamics. By/ Francis Weston Sears, and Gerhard L. Salinger. ( 1975 ) 3// Fundamental of classical and statistical thermodynamics. By/ Bimalendu Narayan Roy. ( 2002 ) 4// Basic Engineering thermodynamics in S I units. By/ Rayner Joel. ( 1974 )
Transcript
Thermodynamics – chapter - 1-
1
References
1// An introduction to thermodynamics, the kinetic theory of gases,
and statistical mechanics.
By/ Francis Weston Sears. ( 1953 )
2// Thermodynamics, kinetic theory, and statistical
thermodynamics.
By/ Francis Weston Sears, and Gerhard L. Salinger. ( 1975 )
3// Fundamental of classical and statistical thermodynamics.
By/ Bimalendu Narayan Roy. ( 2002 )
4// Basic Engineering thermodynamics in S I units.
By/ Rayner Joel. ( 1974 )
Thermodynamics – chapter - 1-
2
CHAPTER -1-
Thermodynamic systems
System: A quantity of matter (substances) bounded by some closed surface.
Or the Substance (or substances) involved in physical and / or chemical
changes is known as the system.
There are four types of system in thermodynamics.
1/ Open system: In such a system, exchange of energy and matter occurs
with its surroundings. ∆m ≠ 0, ∆E ≠ 0.
2/ closed system: In such a system, exchange of energy may occur but no
transfer of matter occurs between the system and its surrounding. ∆m = 0,
∆E ≠ 0.
3/ Thermally isolated system: In such a system, no exchange of energy
(in the form of heat) take place. ∆m = 0, ∆E= 0.
4/ Mechanically isolated system: in such a system, no work is done on the
system or by the system.
Real system : Like that of a tank enclosing a certain mass of compressed
liquid or solid.
Ideal system : Any theoretical system treating with pen and paper to
purpose facilitating (making easy ) the thermodynamic problems , such
system no founded like ideal gas .
System boundary : The boundary may be real one like the inner surface of
a tank containing a compressed gas ,or it may be imaginary , like the surface
boundaring a certain mass of fluid flowing a long a pipe line and followed in
imagination as it progresses .
Surroundings: This is defined as the regions outside the boundaries of the
system which may act on the system .
Universe : A system and its surroundings together are said to constitute a
universe .
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Isolated system : No energy interchange with the surroundings can take
place .
Adiabatic wall : No heat interchange through the wall .
Diathermic wall : Heat interchange through the wall . the temperature is
the same at in and out of the wall .
Process : The actual change that occurs in a system and the manner of its
occurrence is known as the process . A process may be physical or chemical.
Magnetization of an iron bar is a physical process, but rusting of iron is a
chemical process.
Reversible process: In order that a process be thermo dynamically
reversible it must be carried out very slowly (infinitesimally slowly) so that
the system remains in temperature and pressure equilibrium with its
surroundings. A system undergoing such a change can be completely restored
to its initial state.
Irreversible process : In such a process a property of the system differs by
a finite amount from one instant to another and the system cannot return to
its original state. Such processes are real or natural processes.
Spontaneous process: A spontaneous process is one which takes place a
given set of conditions without application of any force. E.g. spreading of
solute through solvent from regions of high concentration to regions of low
concentration. Such processes are also irreversible process.
Isothermal process: When a reversible process occurs at a constant
temperature (i.e. no change in temperature occurs), it is said to be an
isothermal process. In such a process an exchange of heat between the system
and its surroundings occurs to maintain the temperature constant. T = const.
Adiabatic process: An adiabatic process is thermally isolated so that no
heat can enter or leave the system. In the case of a gas undergoing expansion
or compression, the temperature and the volume adjust themselves to
maintain equilibrium as the pressure is changed. The system dose external
work but, because it is thermally insulated, the necessary energy comes from
the kinetic energy of the gas molecules. As the kinetic energy of the gas
molecules decreases, there is a corresponding decrease in temperature. When
a gas is compressed adiabatically, there is a rise in temperature. The essential
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characteristic is that no heat is absorbed in an adiabatic process. Q = const.
Isentropic process: A reversible adiabatic process is called an isentropic
process.
Isobaric process: Iso means "same" and baros means "weight" and hence
an isobaric process is a constant pressure process, i.e. a process carried out at
a constant pressure. P = const.
Isochoric process: The Greek word "chora" means place. So an isochoric
process is one where the volume remains constant throughout the process, or
in other words the process is carried out at constant volume. V = const.
Cyclic process: If the initial state is designated by 1 and the final state by 2,
and if states 1 and 2 coincide , then the process is called a cyclic process . This
process leads from a given state through sequence of changes back to the
original state.
Macroscopic properties: These are the properties of matter which are
obvious to us and they are , naturally , the first features that we use to
describe a physical situation . Examples are volume , pressure and
temperature .
Thermal equilibrium : When two systems are in contact and there is no
change in thermal behavior , the systems are said to be in thermal
equilibrium. For example, when a hot metal wire is immersed in cold water,
the wire is found to shorten , and the water changes its density. These changes
are caused by the exchange of heat. When there are no further changes, it is
said that thermal equilibrium exits.
Thermal interactions: Interactions that cause equalization of the
temperature but are not of a mechanical, chemical, electrical or similar
nature are called thermal interactions. Such interactions may, of course, be
the source of mechanical, electrical or other changes.
State: The state of a system is described by specifying the values of all
relevant macroscopic variables, so that the system could be precisely
duplicated from this information. Like P, V, T, U, …….etc
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State variables or state functions: The macroscopic quantities that are
used to specify the state of a thermodynamic system are called the state
variables because their values depend only on the condition or the state of the
thermodynamic system. Volume, temperature, pressure and density are state
variables for a homogeneous system, but work and heat are not state
variables. V, T, P, ρ, m
Equation of state: The relationship between T, P and V of a given amount
of a substance is called the equation of state, which depends, of course, on the
nature of the substance. Mathematically, an equation of state may be
denoted by:
),,( nPTfV ---------- ( 1 )
V is a function of T, P, and n ( number of moles )
Extensive variables: Those variables that are proportional to the amount
of matter are called extensive variables, e.g. V volume, heat capacity, entropy,
m, charge, magnetization, internal energy, kinetic energy, potential energy.
Intensive variables: Those variables that are independent of the amount
of matter are called intensive variables, e.g. P, T, ρ density, ɳ viscosity, ʋ
specific volume, v velocity, specific enthalpy, thermal conductivity, u.
ʋ = V/n , ʋ is intensive, V extensive, and n no. of mols.
Or u = U/m, ʋ is intensive, U extensive, and m mass.
Equilibrium state: This is a state of a system in which the state variables,
such as T, P, and V, have values that are uniform and constant throughout
the whole system.
Heat: This is a form of energy mainly due to temperature. Heat can be
transferred solely because of a temperature difference between a system and
its surrounding; it usually produces a rise in temperature when it enters a
system. This dose not necessarily mean that temperature changes can be
brought about only by the transfer of heat. This implication is correct,
however, if no work is involved in the process. Heat is denoted by Q or q and
it is considered positive when it is added to the system. The unit of heat is the
Joule.
Energy: This defined as the capacity for doing work. Normally, it is
denoted by U and its units are the erg, Joule, and calorie. There are several
types of energy, namely potential energy, kinetic energy, internal energy,
external energy, etc. Internal and external energies have importance in
thermodynamics.
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Internal energy: This is the energy possessed by all substances in varying
amounts according to the motion and special arrangement of the particles
making up the atoms and molecules. Its absolute value cannot be measured
for a given system but its increment ( ΔU ) is +ive when the internal energy of
a system increases. The increase (ΔU ) in internal energy when a system
changes from state A to state B.
ΔU = UB - UA ----------- ( 2 )
External energy: This is the product of the P and V of a system. It can be
regarded as the energy a substance possesses by virtue of the space it
occupies.
The laws of thermodynamics
Classical thermodynamics is based on the four laws of thermodynamics. In
thermodynamics we are concerned with the behavior of vast quantities of
particles in the substances that we study. The laws of thermodynamics are the
laws of the generalized behavior of the particles. These laws are as follows:
1// The zeroth law which deals with temperature and temperature scale; this
law is seldom considered because similar consideration in terms of the second
law is possible.
2// The first law deals with macroscopic properties. Work, energy, enthalpy,
etc.
3// The second law mainly deals with entropy, a property most fundamentally
responsible for the behavior of matter.
4// The third law deals with the determination of entropy.
Scope of thermodynamics
Thermodynamics is an experimental science based on a small number of
principles that are generalizations made from experience. It is concerned only
with macroscopic or large –scale properties of matter and it makes no
hypotheses about the small-scale or microscopic structure of matter. From
the principles of thermodynamics one can derive general relations between
such quantities as coefficients of expansion, compressibilities, specific heat
capacities, ….
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The principles of thermodynamics also tells us which few of these relations
must be determined experimentally in order to completely specify all the
properties of the system.
The science of thermodynamics had its start in the early part of the
nineteenth century, primarily as a result of attempts to improve the
efficiencies of steam engines, devices into which there is an input in the form
of heat, and whose output is mechanical work. Thus as the name implies,
thermodynamics was concerned with both thermal and mechanical, or
dynamical, concepts.
The principles of thermodynamics are now used by engineers in the design
of internal combustion engines, conventional and nuclear power stations,
refrigeration and air-conditioning systems, and propulsion systems for
rockets, missiles, aircraft, ships, and land vehicles.
Pressure:
pressure is defined as force per unit area.
A
FP ----------- ( 3 )
Where F is force in Newton s ( N ), A is area in meters ( m2 ).
1 bar = 105 Nm-2 = 106 dyne Cm-2 ,
1 μ bar = 10-1 Nm-2 = 1 dyne Cm-2.
A pressure of 1 standard atmosphere ( atm. ) is defined as the pressure
produced by a vertical column of mercury exactly 76 Cm in height, of density
ρ =13.5951 g /Cm3,
At a point where g has its standard value of 980.665 Cm /sec2.
From the equation
P = ρgh we find
1 standard atmosphere ( atm. ) = 1.01325 X 106 dyne / Cm2 = 1.01325 X 105
Nm-2
hence 1 atm. ~ 1 bar, 1 μ bar ~ 10-6 atm.
1 Torr ( named after Torricelli ) = 1 mm – Hg = 133.3 Nm-2
1 atm. = 76 Cm – Hg = 760 mm – Hg = 760 Torr.
Processes: Any change in the thermodynamic coordinates of a system is
called a processes.
We shall give a few illustrations of reversible and irreversible processes.
Consider a gas in a cylinder provided with a movable piston. If the piston is
pushed down very rapidly, the P, T, and ρ immediately below the piston
and the process is irreversible. To compress the gas reversibly, the piston
must be pushed down very slowly to avoid turbulence and allow time for the
P, and T to become the same at all points.
Thermodynamics – chapter - 1-
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Suppose we wish to heat a beaker of water from a T1 to T2. The water
could be heated by placing it over a gas flame. This process is highly
irreversible, because the temperature of the flame is much greater than that
of the water and the water immediately over the flame is much hotter than at
other points. To heat the water reversibly from T1 to T2 we require a
number of other bodies at temperatures T1 + dT, T1 +2dT, T1 + 3dT,
………………. T2 - 2dT, T2 – dT, T2 , as illustrated in Fig. These bodies might
be large water tanks, containing enough water so that the flow of a small
quantity of heat from each one to the beaker will not alter appreciably the
temperature of the water in the tank. We shall speak of such bodies as heat
reservoirs. All actual processes are irreversible, because they take place with
finite differences of pressure and / or temperature between parts of a system,
or between the system and its surroundings. Nevertheless, the concept of a
reversible process is a useful and important one in thermodynamics.
Temperature and thermometry
To understand the meaning of temperature it is necessary first to refer to
the human sense of feeling. It is common experience to talk about some things
feeling hot and other things feeling cold. Feeling, there fore, is not
particularly satisfactory where a high degree of accuracy is required. A great
many devices, both ancient and modern, have been designed and made for
this purpose. Each device uses the effect that hotness or coldness has on some
particular substance as the means by which the degree of hotness or coldness
is measured. A scale of hotness or coldness must be devised, however, such
that each device will record the same degree of hotness or coldness when used
in the same conditions. Having fixed a scale, it is useful to have a single word
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to denote reference to this scale. The word is temperature and the scale is
called the temperature scale. The subject of temperature investigation is
called thermometry.
Now suppose we have two isolated systems, both in thermodynamic
equilibrium. To determine whether they are at the same temperature, we
remove the thermal insulating material from a portion of the surface of both
and bring these portions of the surfaces in contact. If no observable changes
take place in the thermodynamic coordinates of either system, the two are at
the same temperature. ( Although we have not as yet defined the term heat,
we may use it at this point and say that when two systems are at the same
temperature there will be no flow of heat from one to other when the two are
brought in contact.)
Suppose that system ( A ) is at the same temperature as system ( B ), as
determined by the preceding test, and that ( A ) is also at the same
temperature as system ( C ). Then we find by the same test that ( B ) and ( C )
are at the same temperature. That is, when two systems are at the same
temperature as a third, they are at the same temperature as each other. This
statement is sometimes called the Zeroth law of thermodynamics.
If we want to know when two beakers of water are at the same
temperature, it is unnecessary to bring them into contact and see if their
thermodynamic coordinates change with time. We insert a thermometer (
system A ) in one beaker ( system B ) and wait until the length of the mercury
column in the capillary ( a thermodynamic coordinate ) becomes constant.
The thermometer then has the same temperature as the water in this beaker.
We then repeat the procedure with the other beaker
( system C ). If the temperature readings are the same, we infer that the
temperatures of the beakers are the same and experiment shows that they
are; that is, if the two beakers are brought in to thermal contact, no changes
in their measurable properties take place.
Thermometry
The branch of heat relating to the measurement of temperature of a body is
called thermometry and the instrument used to measure temperature is
called a thermometer. The essential requisites of a thermometer are:
1/ Construction: The variation of physical properties of a substance with change in
temperature are used in the construction of a thermometer. The choice of the
thermometric substance which defines both the matter and its state chosen,
i.e. solid, liquid or gas or physical property used, are determined by the range
of temperature to be measured as well as the accuracy of the result desired.
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2/ Calibration: When a thermometer is constructed it should be properly calibrated. The
standard fixed points are selected for calibrating a thermometer. Melting
point of ice, boiling point of water, melting point of silver and melting point of
gold are taken as fixed points. The scales are built by dividing the interval
between the two fixed points into equal parts.
3/ Sensitiveness: The instrument after construction and calibration should be sensitive. For
this purpose:
a/ it can detect even small changes in temperature,
b/ it shows the temperature of a body in a short time and
c/ the thermal capacity of the substance used should be very low so that it
dose not take much heat for its own heating from the body whose
temperature is to be measured.
The common temperature scales used in most scientific work
in many countries are:
1/ Centigrade (or Celsius) scale. (1742).
The ice point is marked as ( 0 Co) and steam point as ( 100 Co ) and the
interval is divided into ( 100 ) equal parts. Each of these divisions is called one
degree centigrade and is represented as ( 1 Co ).
2/ Fahrenheit scale. ( 1720 ).
The ice point is marked ( 32 Fo ) and the steam point ( 212 Fo ) and the
interval is divided into ( 180 ) equal parts. Each division is called one degree
Fahrenheit and is represented as ( 1 Fo ). It appears that Fahrenheit chose (
32o ) for the ice – point, because he found with a freezing mixture that the
maximum frost temperature was
( 32o ) below the temperature of ice.
3/ The Reaumur scale.
This scale was suggested by Reaumur and is used for domestic purposes,
chiefly in Germany. The interval between the two fixed points is divided in to
( 80 ) equal parts, the lower point being marked ( 0 Ro) and the upper one ( 80
Ro), 1 Ro.
The relation between the above three scales are:
C : F – 32 : R : 100 : 180 : 80, or 80180
32
100
RFC
------- ( 4 )
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Any one scale can be readily converted into the corresponding ones on
others.
4/ Absolute temperature scale:
There is no upper limit on temperature but there is a definite lower limit
called the absolute zero of temperature.
Absolute zero = - 273.15 Co = - 459.67 Fo
In laboratory it has been possible to reach temperatures within a few
millionths degree of absolute zero. The absolute zero is thus defined as the
temperature of a body that is incapable of giving any thermal energy. An
absolute scale is thus a scale in which absolute zero is taken as the zero of the
scale. The absolute scale in which the temperatures are measured from
absolute zero in centigrade – size degrees is known as Kelvin scale. Since
absolute zero is ( - 273 Co) a temperature on Kelvin scale is expressed in ( K)
by adding ( 273 ) to the value in ( Co). Thus
Absolute zero = 0 K, 0 Co = 273 K.
5/ Rankine scale:
Is used in engineering practice, is known as Rankine scale since. Absolute
zero is ( - 460 Fo), a temperature may be expressed in ( R/o) by adding
( 460 ) to the value in ( Fo ), the relation between various scale for conversion
of temperature is as given below:
180
492
100
273
80
0
180
32
100
0
RKRFC ------- ( 5 )
Types of thermometers
There are different kinds of thermometers in use may be broadly classified
as follows:-
1/ Liquid thermometers.
These are based on the thermal expansion of liquids such as mercury, alcohol,
etc.
2/ Gas thermometers. These are based on this principle of change in pressure or volume with
change in thermometer, e.g., calendar's constant pressure thermometer,
constant volume hydrogen thermometer etc.
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3/ Resistance thermometers. These depend on the principle of change of resistance with thermometer. e.g.
platinum resistance thermometer.
4/ Thermo – electric thermometers. These are based on the principle of thermo – electricity, i.e., production of
thermo – e.m.f. in a thermo – couple when the two junctions are at different
temperatures.
The various thermocouples commonly used are :-
a/ copper and constantan. b/ iron and constantan.
c/ chromel and constantan. d/ chromel and alumel.
e/ platinum and Rhodium.
5/ Radiation thermometers. These are based on the quantity of heat radiations Emitted by a body e.g.
furnaces. These instruments are known as pyrometer.
6/ Vapour pressure thermometers. These are based on the principle of change of vapour pressure with change in
temperature. These are used to measure low temperatures. e.g., helium
vapour pressure thermometer etc.
7/ Magnetic thermometers. These temperatures are based on the principle of change in the susceptibility
of a substance with temperature. These thermometers are useful of measuring
low temperatures near the absolute zero temperature.
8/ Bimetallic thermometers. These thermometers are based on the principle of expansion of solids. A
bimetallic strip is taken in the form of a spiral. Its one end is fixed and the
other end is attached to a long pointer. The pointer moves on a scale,
calibrated in degrees. These thermometers are used in meteorology for
recording the changes in temperature during the day. They are also used to
measure temperatures at high altitudes.
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Centigrade Absolute Fahrenheit Rankine Reaumur
Celsius Kelvin
C0 K F R/ R
100 373 212 672 80 Steam
Point
20 293 68 528
0 273 32 492 0 Ice
point
- 40 233 - 40 420 - 32
- 273 0 - 460 0 - 218.4 Absolut
Zero
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1/ Liquid thermometers.
To measure a temperature with a given thermometer,
the selected property is measured first with the
thermometer at the temperature of one fixed point,
then at the other fixed point, and finally at the
unknown temperature. Let Xo, X100 and X represent
the values of the measured property at the ice point,
the steam point, and the unknown temperature
respectively. The unknown temperature ( t ) is the
defined by the equation:
0100
0100
XX
XXt
--------- ( 6 )
Let l0, l100, and l represent the distances from some
reference mark on a mercury – in – glass
thermometer to the top of the mercury column in
the capillary when the temperature is at the ice point,
steam point, and unknown temperature.
( see Fig. ) then
0100
0100
ll
llt
----------- ( 7 )
2/Gas thermometers.
a/ At V constant: let P0, P100, and Pt represent the pressures at the ice point,
the steam point, and the unknown temperature respectively. Volume
remaining constant, the pressure increases according to the relation:
