PHYSICAL
CHEMISTRY
MET (201)
LECTURE (3)
GROUP (2)
37
PHYSICAL
CHEMISTRY
MET (201)
CHAPTER (2)
THE FIRST LAW OF
THERMODYNAMICS
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2.1 Introduction
In a frictionless dynamic system of
interacting elastic bodies and under no
gravitational field, kinetic energy is
conserved; in other words,a collision
between two bodies of this system results in
a transfer of kinetic energy from one body to
the other; thus, the total kinetic energy of the
system is unchanged as a result of the
collision.If the dynamic system under the
influence of a gravitational field, the sum of
the kinetic and potential energies of a
moving bodyin this field is constant;this
meansthat, kinetic energy may be converted
to potential energy and vice versa.Also the
sum of the two dynamic energies (kinetic
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and potential) remains constant if two bodies
are collided with each other elastically.
On the other hand, when frictional forces are
operative in the system and 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 relationshipled to the foundations of the
thermodynamic subject.
2.2 The Relationship between
Heat (q) and Work (w)
CountRumford in 1798suggested the first
relation between heat and work; he noticed
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that during the poring ofa cannon atMunich
arsenal, the heat produced was roughly
proportional to the work performed during
the poring process. He suggested that heat is
an invisible fluid (gas) called caloric; he
suggested also that this fluid is resided
between the particles of the substance. In the
caloric theory, the following had been
assumed:
 the temperature of a substance is
determined by the quantity of the
caloric gas which it contains, and
 the amount of caloric per unit mass is
less for smaller particles than for larger
particles.
These two assumptions explain the flow of
heat from bodies with higher temperature to
cold bodies; they explain also thesensible
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heat produced during poring larger pieces to
form smaller pieces( metal turnings ).
The caloric theory was discreditedin 1799
when Humphrey Davy melted two blocks
of ice by rubbing them together. Based on
this experiment, it had been proven thatthe
latent heat necessary to melt icewas
provided by the mechanical work
performed due to rubbing the two blocks
together.
Joulein 1840 conducted experiments in
which work was performed in a certain
quantity of adiabatically contained water(in
other words, the path is defined) and the
resultant temperature rise of water was
measured. He observed that a direct
proportionality exists between work done
and temperature rise. He observed further
that the same proportionality existsno
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matter what means were employed in
work production.The following methods
for work production were used:
1. rotating paddle wheel immersed in
water,
2. electric motor, derived by current
through coil, immersed in water,
3. compressing a cylinder of gas
immersed in water, and
4. rubbing together two metal blocks
immersed in water.
These experiments placed a firm
quantitative
basis
for
thesubject
ofthermodynamics. By considering the
calorie 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, the following equivalence
was found:
1 calorie = 4.184 joule
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The value 4.184 is known as the mechanical
equivalent of heat.
2.3 Internal Energy and the
First Law of Thermodynamics
The development of thermodynamics, from
its early beginnings to its present state, was
achieved as a result of the definition of
convenient thermodynamic functions of
state. In this section the first of these
functionsis introduced. This functionis
named “the internal energy” and it takes the
symbol “U”.
The results of Joule’s experiments put the
basis of thefollowing statement: “the
change of a state of a body inside an
adiabatic enclosure from a given initial
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state to a given final state requires the
same amount of work by whatever mean
the process is carried out”.This statement
is a preliminary formulation of the“First
Law of Thermodynamics”and it is similar
to the following cases.
For a body of mass m when lifted in a gravitational
field g from height h1 to height h2, thework doneon
the body(w) is given by the following relation:
w = potential energy of the body at position 2 −
potential energy of the body at position1
or w = mgh2 − mgh1 = mg(h2 −h1);
also, when a particle with charge q is moved
in an electric field from point at potential𝜑1
to point at potential 𝜑2 , the work doneon the
charged particle is given by the following
relation:
w= electric energy at point 2–
electric energy at point 1
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or w = q𝜑2 − q𝜑1 = q 𝜑2 − 𝜑1
Thus, for the adiabatic experimentations
carried out by joule in which when work
wwas done on a body had changed the
internal energy state of the body from state
𝑈𝐴 to state𝑈𝐵 , it is possible to write the
following relation: w = UB− UA
In applying the following sign convention
for work:the work ispositive if the work is
done on the system,thus UB> UA;and the
workisnegative if the work is done by the
system,
thus
UB<UA.InJoule’s
experimentation, the change in the internal
energy state of the adiabatically contained
water was measured by the temperature
change of water.
The same temperature rise, and hence the
same change ofthe internal energy state,
could have been produced by placing water
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in a thermal contact with a source of heat
and allowing a quantity of heat q to flow
into water. In describing the sign of heat, it
is by convention to assign a positive value
forheat if heat flows into the body
(endothermic process), and anegative value
for heat if heat flows out of the body
(exothermic process); hence,
q = UB –UA
Now for a body which absorbs heat and at
the same time work is performed on it; it is
possible to write the following relation:
∆U = q + w
To prove this simple relation, let us first
consider a thermodynamic systemthat
changes its state 𝑼𝑨 to state 𝑼 𝑩` as a result of
flow of an amount of heat q from a
heatreservoir to the system;thus,
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the following relation can be written:
q = 𝑈𝐵` – UA
If the body is then adiabatically isolated and
is subjected to work w causing a change
from state 𝑈B\ to state UB; thus,
w = UB - 𝑼𝐵` ;
therefore,q + w = (𝑼𝑩` - UA) + (UB - 𝑼𝑩` ),
orq + w = UB - UA ;
thus, ∆U = q + w
For infinitesimal changes, the following
relation can be written:
dU = δq + δw
The previous two equations represent the
mathematical statements of the First Law of
Thermodynamics.
If different paths are used to change the
body state from state 1 to state 2 as shown in
figure
(2.1),which
shows
the
pressure-volume (P-V) relations obtained for
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these different paths, and since the internal
energy is a state functionthe following
relation can be written:
∆U = U2 – U1 ,
regardless of the path followed.
On the other hand, since the value of work is
given by the following relation:
w = -,
the value of work will be dependent on the
path; in other words, the work is not a state
function because it is a path dependent;
accordingly and based on the previous two
equations and the mathematical form of the
First Law of Thermodynamics, the heat is
also a path dependent and therefore it is
not a state function.
Since the internal energy is a state property,
the following functions can be written:
U = 𝒇 (P, V) = 𝒇 (P, T) = 𝒇 (V, T)
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Therefore, the complete differentials of the
internal energy in terms of itspartial
derivatives are given by the following
relations:
𝑑𝑈 = 𝜕𝑈/𝜕𝑃 𝑉 𝑑𝑃 + 𝜕𝑈/𝜕𝑉 𝑃 𝑑𝑉,
or𝑑𝑈 = 𝜕𝑈/𝜕𝑃 𝑇 𝑑𝑃 + 𝜕𝑈/𝜕𝑇 𝑃 𝑑𝑇,
or 𝑑𝑈 = 𝜕𝑈/𝜕𝑉 𝑇 𝑑𝑉 + 𝜕𝑈/𝜕𝑇 𝑉 𝑑𝑇
Figure (2.1): The P-V Relation Obtained in Different Paths (a, b, and c)
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Also, we have the following relations:
2
Since 1 𝑑𝑈 = 𝑈2 − 𝑈1 ,
then dU = 0,
In other words, the cyclic integral equals zero.
Since U is a state function, it is
impossible to have a perpetual motion
machine of the first kind (in other
words,a machine which is based on
creation of energy).
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