Thermodynamics
Thermodynamics
• Thermodynamics is the science of energy
conversion involving heat and other forms of energy,
most notably mechanical work. It studies and
interrelates the macroscopic variables (temperature,
volume and pressure).
• A thermodynamic system (a physical system) is a
precisely defined macroscopic region of the universe
that is studied.
Branches of Thermodynamics
• Classical thermodynamics is the description of the states of
thermodynamical systems at near-equilibrium, using
macroscopic, empirical properties directly measurable in the
laboratory. It is used to model exchanges of energy, work and
heat based on the laws of thermodynamics.
• Statistical mechanics (or statistical thermodynamics) gives
thermodynamics a molecular interpretation. This field relates
the microscopic properties of individual atoms and molecules
to the macroscopic or bulk properties of materials that can be
observed in everyday life, thereby explaining thermodynamics
as a natural result of statistics and mechanics (classical and
quantum) at the microscopic level.
• Chemical thermodynamics is the study of the interrelation
of energy with chemical reactions.
• Biological thermodynamics is the study of energy
transformation in the biological systems.
Equilibrium and non-equilibrium
thermodynamics
• The word equilibrium implies a state of balance. In an
equilibrium state there are no unbalanced potentials, or
driving forces, within the system.
• Equilibrium thermodynamics is the systematic study
of transformations of matter and energy in systems as
they approach equilibrium.
• Most systems found in nature are not in
thermodynamic equilibrium because they are not in
stationary states, and are continuously and
discontinuously subject to flux of matter and energy to
and from other systems. Non-equilibrium
thermodynamics deals with such systems.
Thermodynamic system. Thermodynamic
parameters
A thermodynamic system (a physical system) is a
precisely defined macroscopic region of the universe that
is studied.
A thermodynamic system is characterized and defined by
a set of thermodynamic parameters
• An intensive property (parameter) is a physical
property of a system that does not depend on the system
size or the amount of material in the system
• extensive property (parameter) is one that is additive
for independent, noninteracting subsystems. It is directly
proportional to the amount of material in the system.
Thermodynamic system
• All space in the universe outside
the thermodynamic system is
known as the surroundings (the
environment, or a reservoir). A
system is separated from its
surroundings by a boundary
which may be notional or real,
but which by convention delimits
a finite volume.
• Systems are distinguished
depending on the kinds of
interaction they undergo and the
types of energy they exchange
with the surrounding
environment.
Thermodynamic systems
• Isolated systems are
completely isolated
from their environment.
They do not exchange
heat, work or matter
with their environment.
An example of an
isolated system is a
completely insulated
rigid container, such as
a completely insulated
gas cylinder.
Thermodynamic systems
• Closed systems are able
to exchange energy
(heat and work) but not
matter with their
environment. A
greenhouse is an
example of a closed
system exchanging heat
but not work with its
environment. Whether a
system exchanges heat,
work or both is usually
thought of as a property
of its boundary.
Thermodynamic systems
• Open systems may
exchange any form of
energy as well as
matter with their
environment. A
boundary allowing
matter exchange is
called permeable. The
ocean would be an
example of an open
system.
Internal energy
• Internal 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.
• The internal energy is the total energy contained in a
thermodynamic system. It is the energy necessary to
create the system, but excludes the energy associated
with a move as a whole, or due to external force fields.
Internal energy has two major components, kinetic
energy and potential energy.
• For an ideal monoatomic gas, this is just the translational
kinetic energy of the linear motion of the "hard sphere"
type atoms. However, for polyatomic gases there is
rotational and vibrational kinetic energy as well.
System Work
• When work is done by a
thermodynamic system, it is
ususlly a gas that is doing the
work. The work done by a gas at
constant pressure is:
A  pV
• For non-constant pressure, the
work can be visualized as the
area under the pressure-volume
curve which represents the
process taking place. The more
general expression for work done
V2
is:
A 

V1
pdV
Heat Transfer
Heat is energy transferred from one body or
thermodynamic system to another due to thermal
contact when the systems are at different temperatures.
Heat Conduction
Conduction is heat transfer by means of
molecular agitation within a material without
any motion of the material as a whole. For
heat transfer between two plane surfaces,
such as heat loss through the wall of a house,
the rate of conduction heat transfer is:
Q
t

kS (T hot  T cold )
d
Heat Transfer
Heat Convection
• Convection is heat transfer by mass motion of a fluid
such as air or water when the heated fluid is caused to
move away from the source of heat, carrying energy
with it.
Heat Transfer
Heat Radiation
• Radiation is heat transfer by the emission of
electromagnetic waves which carry energy away from the
emitting object. For ordinary temperatures (less than red
hot"), the radiation is in the infrared region of the
electromagnetic spectrum. The relationship governing
radiation from hot objects is called the StefanBoltzmann law:
4
4
P  e  S (T r  T s )
where P is net radiated power, heat Q transferred in
unit time t,
σ – Stefan’s constant, σ=5.6703x10-8 Watt/m2 k4
S – radiating area,
Tr – absolute temperature of radiator,
Ts – absolute temperature of surroundings,
e - emissivity (=1 for ideal radiator – black body)
Heat Transfer
Heat Transfer by
Vaporization
• If part of a liquid evaporates,
it cools the liquid remaining
behind because it must extract
the necessary heat of
vaporization from that liquid
in order to make the phase
change to the gaseous state. It
is therefore an important
means of heat transfer in
certain circumstances, such as
the cooling of the human
body when it is subjected to
ambient temperatures above
the normal body temperature.
Q
t

mL
t
where m is mass of liquid
L - heat of vaporization at
liquid boiling point
First law of thermodynamics
• The first law of thermodynamics is the application of
the conservation of energy principle to heat and
thermodynamic processes:
Q  U  A
Heat added to the thermodynamic system goes to
change the internal energy and to do the work by
the system.
First law of thermodynamics
The internal energy of a system can be changed by
heating the system or by doing work on it.
 U  Q  A
• If the system is isolated, its internal energy cannot
change.
Heat Engine
• A heat engine is a system that
performs the conversion of heat to
mechanical work. A heat "source"
generates thermal energy that
brings the working substance to the
high temperature state. The
working substance generates work
in the "working body" of the
engine while transferring heat to
the cold reservoir until it reaches
a low temperature state. During
this process some of the thermal
energy is converted into work by
exploiting the properties of the
working substance. The working
substance can be any system with a
non-zero heat capacity, but it
usually is a gas or liquid.
Hot reservoir
Qin
Working body
Energy intake
A=Qin-Qout
Qout Energy exhaust
Cold reservoir
Heat Engine
• Qin is the heat flow from the hot reservoir to the
engine
• Qout is the heat flow from the engine to the cold
reservoir.
• The work done by the heat engine is the difference
between Qin and Qout.
• Heat engine efficiency:
 
A
Q in

Q in  Q out
Q in
Entropy as a Measure of the Multiplicity of a
System
The probability of finding a system in a given state
depends upon the multiplicity of that state. That is to
say, it is proportional to the number of ways you can
produce that state. Here a "state" is defined by some
measurable property which would allow you to
distinguish it from other states. Entropy:
S  k ln W
where k is Boltzmann's constant, W is the number of
microstates The k is included as part of the historical
definition of entropy and gives the units J/K in the SI
system of units. The logarithm is used to make the
defined entropy of reasonable size. The multiplicity
for ordinary collections of matter are on the order of
Avogadro's number, so using the logarithm of the
multiplicity is convenient.
Entropy in Terms of Heat and Temperature
• A the change in entropy can be described as the heat
added per unit temperature
ΔS = Q/T
where S is the change in entropy,
Q is the heat flow into or out of a system, and T is the
absolute temperature in degrees Kelvin (K).
• This is often a sufficient definition of entropy if you
don't need to know about the microscopic details. It can
be integrated to calculate the change in entropy during a
part of an engine cycle.
• The concept of entropy (S) gives us a more quantitative
way to describe the tendency for energy to flow in a
particular direction.
Entropy
a state variable whose change is defined
Entropy: for a reversible process at T where Q is
the heat absorbed.
a measure of the amount of energy
Entropy:
which is unavailable to do work.
Entropy: a measure of the disorder of a system.
a measure of the multiplicity of a
Entropy:
system.
Thermodynamic Potentials
• Four quantities called "thermodynamic
potentials" are useful in the chemical
thermodynamics of reactions and noncyclic processes. They are internal
energy, the enthalpy, the Helmholtz
free energy and the Gibbs free energy.
The four thermodynamic potentials are
related by offsets of the "energy from
the environment" term TS and the
"expansion work" term PV. A
mnemonic diagram help you keep
track of the relationships between the
four thermodynamic potentials.
Enthalpy
• Enthalpy is a thermodynamic potential. It is a state
function since it is defined in terms of three other
precisely definable state variables, and it is an
extensive quantity. Enthalpy is a measure of the total
energy of a thermodynamic system. It includes the
internal energy U, which is the energy required to
create a system, and the amount of energy required to
make room for it by displacing its environment and
establishing its volume V and pressure P.
H = U + PV
• It is somewhat parallel to the first law of
thermodynamics for a constant pressure system
Q = ΔU + PΔV, since in this case Q=ΔH
Thermodynamic free energy
• The thermodynamic free energy is the amount of work
that a thermodynamic system can perform. The concept is
useful in the thermodynamics of chemical or thermal
processes in engineering and science. The free energy is
the internal energy of a system less the amount of energy
that cannot be used to perform work. This unusable
energy is given by the entropy of a system multiplied by
the temperature of the system. Free energy is that portion
of any first-law energy that is available to perform
thermodynamic work; i.e., work mediated by thermal
energy. Free energy is subject to irreversible loss in the
course of such work. Since a first-law energy is always
conserved, it is evident that free energy is an expendable,
second-law kind of energy that can perform work within
finite amounts of time. Several free energy functions may
be formulated based on system criteria.
Free energy functions
• The historically earlier Helmholtz free energy is
defined as
•Its change is equal to the amount of reversible work
done on, or obtainable from, a system at constant T. It is
"work content“. Since it makes no reference to any
quantities involved in work (such as p and V), the
Helmholtz function is completely general: its decrease is
the maximum amount of work which can be done by a
system, and it can increase at most by the amount of
work done on a system.
Free energy functions
• The Gibbs free energy
The internal energy U might be thought of as the energy required to
create a system in the absence of changes in temperature or volume.
But as discussed in defining enthalpy, an additional amount of work PV
must be done if the system is created from a very small volume in order
to "create room" for the system. As discussed in defining the Helmholtz
free energy, an environment at constant temperature T will contribute
an amount TS to the system, reducing the overall investment necessary
for creating the system. This net energy contribution for a system
created in environment temperature T from a negligible initial volume
is the Gibbs free energy.
Free energy functions
• Historically, these energy terms have been used inconsistently. In
physics, free energy most often refers to the Helmholtz free energy,
while in chemistry, free energy most often refers to the Gibbs free
energy.
• For processes involving a system at constant pressure p and
temperature T, the Gibbs free energy is the most useful because,
in addition to subsuming any entropy change due merely to heat, it
does the same for the pdV work needed to "make space for
additional molecules" produced by various processes. (Hence its
utility to solution-phase chemists, including biochemists.) The
Helmholtz free energy has a special theoretical importance since it
is proportional to the logarithm of the partition function for the
canonical ensemble in statistical mechanics. (Hence its utility to
physicists; and to gas-phase chemists and engineers, who do not
want to ignore pdV work.)
The second law of thermodynamics
Clausius statement
• The second law of thermodynamics describes the flow of
energy in nature in processes which are irreversible.
• The second law of thermodynamics may be expressed in
many specific ways.
Second Law and Refrigerator
• It is not possible for heat to flow from a colder body
to a warmer body without any work having been
done to accomplish this flow. Energy will not flow
spontaneously from a low temperature object to a
higher temperature object.
• This precludes a perfect refrigerator.
• The statements about refrigerators apply to air conditioners
Kelvin-Planck statement
Second Law and Heat Engine
• It is impossible to extract an amount of heat from a
hot reservoir and use it all to do work. Some amount
of heat must be exhausted to a cold reservoir.
• It meams that the efficiency of a heat engine cycle is
never 100%.
• This precludes a perfect heat engine.
Second Law and Entropy
• The second law of thermodynamics is closely related
to the concept of entropy, or the disorder created
during a thermodynamic process.
• In any cyclic process the entropy will either increase
or remain the same.
• Since entropy gives information about the evolution
of an isolated system with time, it is said to give us
the direction of "time's arrow“.
Other Second Law Formulations
• In practical applications, this law means that:
• Any heat engine or similar device based upon
the principles of thermodynamics cannot, even
in theory, be 100% efficient.
Equivalence of the statements
Derive Kelvin Statement from Clausius
Statement
Suppose there is an engine violating the Kelvin
statement: i.e.,one that drains heat and converts
it completely into work in a cyclic fashion
without any other result. Now pair it with a
reversed Carnot engine as shown by the graph.
The net and sole effect of this newly created
engine consisting of the two engines mentioned
is transferring heat from the cooler reservoir to
the hotter one, which violates the Clausius
statement. Thus a violation of the Kelvin
statement implies a violation of the Clausius
statement, i.e. the Clausius statement implies
the Kelvin statement. We can prove in a similar
manner that the Kelvin statement implies the
Clausius statement, and hence the two are
equivalent.