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THERMODYNAMICS - I
CHAPTER 3
SECOND LAW OF THERMODYNAMICS
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The First Law of Thermodynamics
• Cannot be derived from any fundamental principle.
• Has never failed an experimental test from its
inception.
• Comes in two versions:
- within a system: simply called the “ 1st law”
- between system and surroundings or two
systems: “Law of Conservation of Energy”
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Conversion of Work into Heat
River
Electrical
Resistor
• Electric resistor is immersed in a river and heater
is switched on. Electrical work is converted into
heat.
• Water absorbs the heat completely and the
resistor does not store any energy. Work is
completely converted into heat.
• Work is a high grade energy whereas heat is a
low grade energy
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Conversion of Work into Heat
Example: A steam turbine power plant
Normally
WP
‹‹ WT
and QL
›› 2/3 QH
This means that
W net
‹ 1/3 QH
if the entire heat
input QH
were converted, WHY?
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Where the First Law is inadequate
• Consider an ISOLATED system consisting of
two rigid subsystems of different temperatures
that communicate thermally:
• 1st law yields:
• Either Q1
or Q2
must be negative (i.e. one of
the two arrows must be reversed).
• 1st law cannot tell which one is negative. But
2nd law can.
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Limitations imposed by the First law of
thermodynamics
If you are constrained to put
a waterwheel half-way up
the waterfall, then you can
extract at the most half of
the available energy
If a 600 K heat engine
must exhaust heat at 300
K, then it can be at the
most 50% efficient
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A system that undergoes a cycle involving
work and heat
When W and Q are both negative the cycle is
possible but when both are positive the cycle is
not possible.
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The First law does not answer many questions
• Why there can’t be complete transformation of
heat into work but work can be completely
transformed into heat?
• Why some processes can proceed in one
direction but not in the other?
• Why it is possible for certain processes to take
place but impossible for other processes to
occur?
The second law will provide answer to these
questions.
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Thermal Reservoir
• A hypothetical body with a relatively large
capacity for thermal energy that can supply or
absorb finite amount of heat without
undergoing change in its temperature.
• Ex: Atmospheric air, Oceans, Rivers and
Industrial furnaces etc.
• Source: The thermal reservoir which supplies
heat
• Sink: The thermal reservoir which receives
heat
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Heat Engines
• A heat engine is a continuously operating
thermodynamic system at the boundary of
which there are heat and work interactions.
• A heat engine may be in the form of a mass of
gas confined in a cylinder and piston device or
a mass of water moving in a steady flow
through a steam power plant.
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A steam turbine power plant is a Heat Engine
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A closed cycle gas turbine engine-is a Heat Engine
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A Open cycle gas turbine engine is not a Heat Engine
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The reversed Heat Engines - Refrigerators and Heat
Pumps
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Heat Engines & Heat Pumps
Representation of:
Heat Engine Heat Pump
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Heat Engine Efficiency:
• Thermal efficiency of a heat engine is defined
as the ratio of the net work output to the heat
input. i.e.
• Efficiency is a measure of the excellence of the
heat engine.
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Coefficient of Performance:
Coefficient of performance of a Refrigerator is
defined as the ratio of the cooling effect to the work
input. i.e.
Coefficient of performance of a Heat Pump is
defined as the ratio of the Heating effect to the work
input. i.e.
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Kelvin-Planck statement of the second law
It is impossible to extract an amount of heat QH
from a hot reservoir and use it all to do work Wnet
Some amount of heat QC
must be exhausted to a
cold reservoir.
OR
It is impossible for a heat engine to produce net
work in a complete cycle if it exchanges heat only
with bodies at a single temperature.
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Extracting heat QH
and using it
all to do work W would
constitute a perfect heat engine,
forbidden by the second law.
POSSIBLE
IMPOSSIBLE
All heat engines must lose some heat to the environment
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Clausius statement of the Second law
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.
OR
Heat cannot flow of itself from a body at lower
temperature to a body at higher temperature.
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Spontaneous flow of heat from a cold
area to a hot area would constitute a
perfect refrigerator, forbidden by the
second law
All real refrigerators
require work to get heat to
flow from a cold area to a
warmer area
IMPOSSIBLE
POSSIBLE
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Kelvin-Planck & Clausius statement are
equivalent
The Kelvin-Planck and Clausius statements
appear to be different, they are really equivalent in
the sense that Violation of one statement results in
the violation of the other
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Violation of K-P statement results in the violation
of Clausius statement
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Violation of Clausius statement results in the
violation of K-P statement
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Perpetual Motion Machines
Perpetual Motion Machine of First Kind-PMMKI (
Impossible to construct, violates First law)
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Perpetual Motion Machine of Second
Kind-PMMK II
• Heat engine works with a
single thermal reservoir,
converts all the heat
supplied into work i.e. W =
QH
and QL
= 0, Efficiency =
100 %
• Impossible to construct,
violates the second law of
thermodynamics.
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Processes
Reversible or Ideal Processes
Irreversible or Natural Processes
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Reversible Process
• It is performed in such a way that at the
conclusion of the process, both SYSTEM and
SURROUNDINGS may be restored to their initial
states, without producing any changes in the rest
of the UNIVERSE. It is an ideal Process.
• A process is reversible if, after the process has
been completed, means can be found to restore
the system and all elements of its surroundings to
their respective initial states.
In nature no real process is truly reversible
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Reversible Process
Examples:
• Frictionless relative motion.
• Extension and compression of a spring.
• Frictionless adiabatic expansion or compression of
fluid.
• Polytropic expansion or compression etc
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Condition for a process to be reversible
• There should be no friction.
• There should be no heat transfer across finite
temperature difference.
• Both the systems and surroundings be stored to
original sate after the process is reversed.
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Why such fictitious processes need to be
considered in the study of thermodynamics ?
• They are easy to analyze since a system passes
through a series of equilibrium states during a
reversible process.
• They serve as idealized models to which actual
processes can be compared.
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Representation of a reversible process
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Irreversible Process
• Any process which is not reversible is an
irreversible process.
• The irreversibility of a process may be due to:
- Lack of equilibrium during the process.
- Involvement of dissipative effects.
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Examples:
• Movement of solids with friction.
• Flow of viscous fluids in pipes and passages.
• Mixing of two different substances.
• Heat transfer through a finite temperature
difference.
• Combustion process.
• Free expansion etc.
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Irreversible Processes
Irreversibility due to
dissipative effects like friction
Free expansion
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Representation of an irreversible process
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Proof that heat transfer through a finite
temperature difference is irreversible
Heat transfer through a finite
temperature difference
Heat transfer through a finite
temperature difference is irreversible
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Definitions:
• Reversible Cycle: One in which all the
processes are reversible.
• Irreversible Cycle: One which contains at least
one irreversible process.
• Reversible Engine: An engine which works in a
reversible cycle.
• Irreversible Engine: An engine which works in
an irreversible cycle.
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The Carnot Cycle and Efficiency
Processes
1. A reversible Isothermal
process (heat addition)
2. A reversible adiabatic
process (Expansion)
3. A reversible Isothermal
process (heat rejection)
4. A reversible adiabatic
process (Compression)
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Carnot engine –Steady Flow System
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Carnot cycle on a property diagram
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Efficiency:
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Reversed Carnot engine–Steady Flow process
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Coefficient of Performance:
Reversible Heat Engine:
A Heat Engine which engages in heat transfer
with two systems of fixed, but different
temperature, is reversible if its efficiency when
operating directly equal to the reciprocal of its
COEFFICIENT OF PERFORMANCE when
operating as a heat pump.
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Carnot Principles
First Principle:
The efficiency of an irreversible heat engine is
always less than the efficiency of a reversible
engine operating between the same two thermal
reservoirs (CARNOT THEOREM)
η th,irrev
‹ η th,rev
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Second Principle:
The efficiencies of all the reversible heat
engines operating between the same two
thermal reservoirs are the same.
If we consider two reversible engines A and B
operating between the same two thermal
reservoirs, then
η th,rev A
= η th,rev B
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Proof of Carnot’s first Principle
Therefore
ηI
≤ ηR
ηR
is MAXIMUM and is called as Carnot
Theorem
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Proof of Carnot’s Second Principle
Let two reversible
engines R1
and R2
work between the
same two thermal
reservoirs having
temperatures TH
and
TL
.
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We imagine R1
driving R2
backward, then Carnot
theorem states that,
If R2
drives R1
backward, then,
It therefore follows that
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• If this were not so, the more efficient engine
could be used to run the less efficient engine in
the reverse direction and the net result would be
transfer of heat from a body at a low
temperature to a body at a high temperature.
• This is impossible according to the second law.
This is the corollary of Carnot’s theorem.
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Let ηR1
= 50 %, ηR2
= 40 % and R1
drives R2
I
M
P
O
S
S
I
B
L
E
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The absolute Temperature Scale
• A Temperature scale that is independent of the
properties of the substances that are used to
measure temperature is called a
Thermodynamic scale of temperature or The
absolute Temperature Scale or Kelvin Scale.
• It can be defined with the help of reversible
heat engines. The thermal efficiency of a
reversible engine is,
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• If some functional relationship is
assigned between TH
, TL
and QH
,
QL
equation (2) then becomes the
definition of a temperature scale.
• Consider three reversible heat
engines as shown.
• Engines R1 & R2 can be combined
into one reversible engine operating
between the same reservoirs as
engine R3 and thus this combined
engine will have the same efficiency
as engine R3.
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Using equation (2) we can write
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To satisfy this condition, the function must have
the following form:
For a reversible heat engine
This is the only condition that the second law
stipulates on the ratio of heat flows to and from the
reversible heat engines.
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• Since the function φ (T) is completely arbitrary,
several values of it will satisfy equation (4).
• Lord Kelvin first proposed taking φ (T) = T to define
thermodynamic temperature scale as:
• This scale is called the Kelvin scale and the
temperatures on this scale are called absolute
temperatures.
• With equation (5) the thermodynamic scale is not
completely defined, since it gives only a ratio of the
absolute temperatures.
