GROUP (1)
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CHAPTER ONE
INTRODUCTION AND
DEFINITION OF TERMS
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1.1 Introduction
 Matter: matter is defined as the substance which occupies a
definite volume of the space.
 Classical thermodynamics: it is that subject of science
which is concerned with establishing the equilibrium between
a given parts of the matter of the universe, called the system,
and the remaining part of the universe, known as the
environment (or the surroundings).
 The main aim of applied thermodynamics is the determination
of the effect of the pressure and temperature of the
environment on the equilibrium state of a given system.
1.2 The Concept of Thermodynamic State
 The thermodynamic microscopic state of a system is defined
by set of knowledge of mass, velocity, position and modes of
motion of all particles that form the system; the microscopic
state of the system in turn would determine all the properties
of the system.
 It might have seen that an enormous amount of information
might be required to identify the microscopic thermodynamic
state of the system.
 It's found that when a very small number of properties are
fixed, then all of the rest are automatically fixed; for example,
when a simple system, such as a given quantity of substance
of fixed composition is being considered, the fixing of two of
the properties of the system fixes the values of all of other
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

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properties; thus only two properties are independent
variables.
So, the thermodynamic state of a simple system is uniquely
fixed when the values of two independent variables are fixed.
The choice of the two independent variables is purely matter
of convenience.
Properties most amenable to experimental work are the
pressure P and the temperature T of the system.
Now, consider the volume V of the system as a property, the
value of which will be dependent on the value of P and T;
thus we can write:
V = f(P,T)
(1)
The relation between P , V and T for a system is called an
equation of state for the system.
In a three-dimensional diagram, the coordinates of which are
pressure, volume and temperature, the points in the P-V-T
space which represent the equilibrium states of existence of
the system lie on a surface, this is shown in figure(1.1).
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Figure (1.1) : the equilibrium states of the system of
existence of a fixed quantity of gas in
the P-V-T space .
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 Consider a process which moves the system an infinitesimal
distance from state a to state c ; thus :
𝑑𝑉 = 𝑉𝑐 − 𝑉𝑎 = (𝑉𝑐 − 𝑉𝑑 )𝑃 + (𝑉𝑑 − 𝑉𝑎 ) 𝑇
= (𝑉𝑐 − 𝑉𝑏 ) 𝑇 + (𝑉𝑏 − 𝑉𝑎 )𝑃
Thus:
𝜕𝑉
∂V
𝑑𝑉 = ( )
T
𝜕𝑃
dP + ( ) P dT
∂T
(2)
 Thus, the value of ∆𝑉 = 𝑉𝑐 –𝑉𝑎 depends only on 𝑉𝑐 and 𝑉𝑎 and is
independent of the path taken by the system between state a
and state c.
 This is a consequence of the facts that V is a state function
and equation (2) is a perfect differential of the volume V.
1.3 Simple Equilibrium
 Consider the simple system illustrated in figure (1.2); this
system consists of a fixed quantity of a gas contained in a
cylinder fitted with a movable piston.
 The system is at equilibrium state when :
1. The pressure exerted on the gas by by the piston,
Psur,equals the pressure exerted on the piston by the gas,
P,
i.e. the system is under mechanical equilibrium
(Psur = P).
2. The temperature of the gas, T, equals the temperature of
the surroundings, Tsur , providing that the cylinder and
piston materials are a conductor of heat ; under this
condition, we have thermal equilibrium (Tsur = T)
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Figure (1.2) : quantity of a gas contained in a cylinder
fitted with a movable piston .
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 The state of the system is then fixed at state 1 which fixes the
volume at the value V1 such that the state (P1,V1,T1) is
represented by a point that lies on the P-V-T surface in
figure (1.1).
 Changing the pressure exerted by the environment, either by
increasing or decreasing, will cause the piston to move, in or
out; respectively, thus changing the volume of the system to
V2 , i.e. the system state changes from the equilibrium state
(P1,V1,T1) to the equilibrium state (P2,V2,T1) assuming that
the compression or the expansion process is isothermal; of
course, the point (P2,V2,T1) should lie on the P-V-T surface.
 The change of Tsur will cause heat transfer either inward to
the system, if Tsur > T, or outward, if
Tsur < T; causing the
system temperature to change to T2 which lead to moving the
piston such that the system volume changes to V2; thus the
equilibrium state (P1,V1,T1) changes to (P1,V2,T2) both lie on
the P-V-T surface.
 If Psur and Tsur are changed simultaneously, the equilibrium
state of the system (P1,V1,T1) will change to the equilibrium
state (P2,V2,T2) both lie on the P-V-T surface.
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1.4 The Equation of State of an Ideal Gas
 In 1660 Robert Boyle found that, for gases, at constant T :
𝑃 ∝
or :
1
𝑉
𝑃𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
This equation is known as Boyle’s Law which gives the relation
between pressure and volume of a gaseous system at constant
temperature.
 Similarly, the volume-temperature relationship of gases at
constant pressure was first determined experimentally by
Charles in 1787. This relationship, which is known as Charles’s
Law, states that, at constant P:
or :
 In 1802, Joseph Gay-Lussac observed that the coefficient
of thermal expansion, 𝛼, of many gases is constant;𝛼 is
given by:
𝛼=
1
𝑉°
(
𝑉− 𝑉 °
1
𝑇− 𝑇
𝑉°
°) 𝑃 =
9
𝜕𝑉
( )𝑃
𝜕𝑇
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


where 𝑉 ° is the volume of the gas at 0℃ and T° = 0°C, Joseph
Gay-Lussac obtained a value of 1/267 for 𝛼
In 1878, Regnault showed that 𝛼 = 1/273 through more
refined experimentation.
Later on it was found that the behavior of different gases varies
slightly from Boyle’s and Charles’ Laws and from one gas to
another.
Generally, gases with lower boiling points obey Boyle’s and
Charles’ Laws more closely than did gases with higher boiling
points. It was also found that, the laws were more closely
obeyed by all gases as the pressure of the gas was lowered.
Gases under these conditions are named Ideal Gases and for
these ideal gases ∝= 1/273.16 .
This means that at -273.16˚C , the gas volume tends to be zero
and hence the limit of temperature decrease is -273.16˚C, and
this will represent the absolute zero of temperature.
This define an absolute scale of temperature called the ideal
gas temperature scale, Kelvin scale , which is related to the
centigrade scale by the relation :
T(K)=T(˚C) + 273.16
Combination of Boyle’s law and charles’ law yields:
𝑃 𝑉 𝑃° 𝑉°
=
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑇
𝑇°
 Where 𝑷° , 𝑽° , 𝑻° are the value of P , V and T at reference
point, say the standard temperature and pressure (STP) whish
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equal 0˚C and 1 atm . Avogadro has shown that the volume per
one mole of all gases at STP is 22.414 lit ; i.e.
V˚= 22.414 lit /molet
𝑃° 𝑉°
 Thus
=0.082057 lit.atm/K-mole; this constant is termed R
𝑇°
and is known as The Universal Gas Constant.
 Accordingly: for n moles of any ideal gas the equation of state,
is given by :
PV  nRT
1.5 The UNITS of the Universal Gas Constant
R =0.082057
lit.atm/deg-mole
=8.3144
joule/deg-mole
=1.9872
cal/deg-mole
Thus:
1 cal = 4.184 joule
1 lit.atm = 1.013 × 102 joule
 Remember that:
1 joule = 107 erg
1 atm. = 76 cmHg
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= 𝟕𝟔 × 𝟏𝟑. 𝟓𝟒𝟓(𝝆𝑯𝒈 ) × 𝟗𝟖𝟎. 𝟔𝟔𝟓(𝒈)
=1.013 × 106 dynes/𝑐𝑚2 =1.013 × 102 KN/𝑚2
=1.01335 bar
1.6 Extensive and Intensive Properties:
 State variables can be categorized into two types: extensive
and intensive
 Extensive variables are those whose magnitudes depend on
the mass of the system.
 Intensive variables are those whose magnitudes are
independent of the mass of the system (pressure,
temperature , densities ,
V/m
, the molen properties , etc . )
We know that: PV = nRT , thus : Pv = RT ; therefore
V Is extensive variable while v is an intensive variable.
1.7 Homogeneous and Heterogeneous systems
 Homogeneous systems are those which each contains one
phase only: i.e. the system consists of physically, chemically
and structurally uniform state of matter.
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 Heterogeneous systems are those which each consists of
two or more phases; i.e. the physical, chemical, or/and
structural uniformity is missed in the system.
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CHAPTER TWO
THE FIRST LAW OF
THERMODYNAMICS
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2.1 Introduction
 In a frictionless kinetic system of interacting elastic bodies,
kinetic energy is conserved; i.e., a collision between two of
the bodies of this system results in a transfer of kinetic
energy from one to the other; thus, the total kinetic energy of
the system is unchanged as a result of the collision.
 If the kinetic system is in the influence of a gravitational filed ,
thus the sum of the kinetic and potential energies of the
bodies is constant ; however , kinetic energy may be
converted to potential energy and vice versa , but the sum of
the two dynamic energies (kinetic and potential) remains
constant.
 If, however, frictional forces are operative in the system then
with continues collision and interaction among the bodies, the
total dynamic energy of the system decreases and heat is
produced. It is thus reasonable to expect that there is a
relationship between the dynamic energy lost and heat
produced .
 The establishment of this relationship laid to the foundations
for the development of the thermodynamic subject .
2.2 The Relationship Between Heat and Work
 In 1798, Count Rumford suggested the first relation between
heat and work; he noticed that during the boring of a cannon
at the Munich arsenal, the heat produced was roughly
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proportional to the work performed during the boring process.
He suggested that heat is an invisible fluid (gas), called
caloric, which resided between the particles of the
substance. In the caloric theory, it had been assumed that
the temperature of a substance is determined by the quantity
of the caloric gas which it contains; it was also assumed that
the amount of caloric per unit mass is less for smaller
particles than larger particles. These two assumptions explain
the flow of heat from bodies with higher temperature to cold
bodies; and the sensible heat produced during poring larger
pieces to form smaller pieces, metal turnings.
 In 1799, the caloric theory was discredited when Humphrey
Davy melted two blocks of ice by rubbing them together.
Based on this experiment, it had been proven that the latent
heat necessary to melt the ice was provided by the
mechanical work performed due to rubbing the blocks
together.
 In 1840, Joule conducted experiments in which work was
performed in a certain quantity of adiabatically, i.e. the bath is
defined, contained water and measured the resultant
temperature rise of the water. He observed that a direct
proportionality exists between the work done and the
temperature rise. He observed further that the same
proportionality exist, no matter what means were employed in
the work production. Methods for work production used
are:
1. rotating paddle wheel immersed in water.
2. electric motor driving current through coil immersed in
water.
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3. compressing a cylinder of gas immersed in water
4. rubbing together two metal blocks immersed in water
 These experiments placed on a firm quantitative basis for the
thermodynamics subject. By considering the calori as the
heat unit and defining it as the amount of heat required to
raise the temperature of one gram of water from 14.5 ˚C to
15.5 ˚C, it was found that:
1 calori = 4.184 joule
This constant, 4.184, is known as the mechanical equivalent
of heat .
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