Lecture 6
Chapter 7 : Second Law of
Thermodynamics
Introduction
• To explain further the 2nd Law of Thermodynamics
“Processes proceed in a certain
direction but not in the opposite
direction if left to occur naturally.”
HEAT ENGINES AND
REFRIGERATORS
• The 2nd Law of thermodynamics for cycles is
expressed in terms of devices called heat
engines and refrigerators that operate on
thermodynamic cycles.
HEAT ENGINE
– a device that operates in a thermodynamic cycle and does net
positive work due to heat transfer from a high temperature
body to a low temperature body. For this device,
• Wnet = (+) and Qnet = (+).
Thermal Efficiency
The performance of a heat
engine is measured by its thermal
efficiency defined as the ratio of
output ( energy sought = Wnet )
to input ( energy that costs = QH).
Wnet QH QL QL
t 1
QH QH QH
Example
• Heat is transferred to a heat engine from a
furnace at a rate of 80 MW. If the rate of
waste heat rejection to a nearby river is 50
MW, determine the net power output and the
thermal efficiency for this heat engine.
Refrigerator / Heat Pump
• Consider the two systems below that undergo the heat transfer
cycle indicated:
• For the two systems shown, the cycle each should undergo cannot
be completed due to the impossibility of the reverse heat transfer
process - heat transfer from low to high temperature body
• The heat transfer from the low to the high temperature body can
be made possible through a device called a heat pump or
refrigerator.
Refrigerator / Heat Pump
– a device that operates in a thermodynamic
cycle, requires a net work input, and transfers
heat from a low temperature body to a high
temperature body. For this device,
• Wnet = (-) and Qnet = (-).
Refrigerator Coefficient of Performance
• Refrigerator performance is
defined as the ratio of the heat
transfer from the refrigerated
space to the input work to the
compressor
QL QL 1
COP
Wnet QH QL QH / QL 1
Refrigerator / Heat Pump
– a device that operates in a thermodynamic
cycle, requires a net work input, and transfers heat from
a low temperature body to a high temperature body. For
this device,
• Wnet = (-) and Qnet = (-).
Heat Pump Coefficient of
Performance
• Heat pump performance is
defined as the ratio of the heat
transfer to the heated space to
the input work to the
compressor.
QH QH 1
COP '
Wnet QH QL 1 QH / QL
• The food compartment of a refrigerator, is
maintained at 4°C by removing heat from it at
a rate of 360 kJ/min. If the required power
input to the refrigerator is 2 kW, determine (a)
the coefficient of performance of the
refrigerator and (b) the rate of heat rejection
to the room that houses the refrigerator.
• Air conditioners are basically
refrigerators whose refrigerated
space is a room or a building
instead of the food
compartment. A window air-
• conditioning unit cools a room by
absorbing heat from the room air
and discharging it to the outside.
THE 2ND
LAW OF
THERMODYNAMICS
• The concept of a thermal reservoir is defined before stating
the 2nd Law
• Thermal Reservoir – a body to which and from which heat
can be transferred indefinitely without change in temperature
of the body
• a thermal reservoir always remain at constant temperature
• approximated by a body with a large thermal mass, e.g., the
atmosphere, the ocean
A reservoir from which heat is transferred
is also known as a source and
that which receives heat as sink
Kelvin-Planck Statement
– There are two classical statements of the second law based
on the concepts of heat engines and refrigerators/heat
pumps
• Kelvin-Planck Statement
It is impossible to construct a device that
– operates in a thermodynamic cycle and
– produces no effect other than the raising of a weight and
– exchanges heat with a single reservoir
“It is impossible for any device that operates on
a cycle to receive heat from a single reservoir
and produce a net amount of work.”
Kelvin-Planck Statement
• Implications:
• The thermal efficiency of a heat
engine cannot be 100%.
- this is so since η t = W / QH
and W < QH
- a perpetual motion machine of the
second kind is impossible to construct
• For work to be done by the transfer of heat, there must be
two temperature levels, a TH, and TL involved
• - since ηt < 1, or W < QH, some amount of heat
QL < QH has to be rejected to a lower temperature (TL) body.
Clausius Statement
• It is impossible to construct a device that
– Operates in a thermodynamic cycle and
– Produces no effect other than the transfer of heat
from a cooler to a hotter body
• Implications:
• The refrigerator/heat pump
must have work input
• The coefficient of performance
is always less than infinity
– this is so since β = QL / W and W > 0
Observations on the Kelvin-Planck
and Clausius Statements
1. Both are negative statements and their validity rests on
experimental evidence.
2. These two statements of the 2nd Law are equivalent. Their
equivalence is proven by showing that a violation of one implies a
violation of the other.
3. The 2nd Law states that it is impossible to build a perpetual-motion
machine of the second kind.
– It is a device that would extract heat from a source and then convert
this heat completely into other forms of energy, e.g., work.
Question:
• If a heat engine cannot have a thermal efficiency of 100%, what is
the maximum efficiency it can have?
REVERSIBLE AND IRREVERSIBLE
PROCESSES
• The processes that were discussed at the beginning of
this chapter occurred in a certain direction. Once
having taken place, these processes cannot reverse
themselves spontaneously and restore the system to its
initial state.
• For this reason, they are classified as irreversible
processes. Once a cup of hot coffee cools, it will not
heat up by retrieving the heat it lost from the
surroundings. If it could, the surroundings, as well as
the system (coffee), would be restored to their original
condition, and this would be a reversible process.
Reversible Process
• A reversible process is defined as a process that can be
reversed without leaving any trace on the surroundings. That
is, both the system and the surroundings are returned to their
initial states at the end of the reverse process. This is possible
only if the net heat and net work exchange between the
system and the surroundings is zero for the combined
(originaland reverse) process.
Internally and Externally
Reversible Processes
• Internally Reversible Process
• A process that is reversible from the point of view of the system only, or
• A process once having taken place, can be reversed without leaving a
permanent change in the system (only)
• Externally Reversible Process
• A process that is reversible from the point of view of the surroundings only
Irreversibilities
• The factors that cause a process to be
irreversible are called irreversibilities.They
include friction, unrestrained expansion,
mixing of two fluids, heat transfer across a
finite temperature difference, electric
resistance, inelastic deformation of solids, and
chemical reactions. The presence of any of
these effects renders a process irreversible.
Friction
• Friction is a familiar form of irreversibility associated with
bodies in motion. When two bodies in contact are forced to move relative
to each other a friction force that opposes the motion develops at the
interface of these two bodies, and some work is needed to overcome this
friction force. The energy supplied as work is eventually converted to heat
during the process and is transferred to the bodies in contact, as
evidenced by a temperature rise at the interface. When the direction of
the motion is reversed, the bodies are restored to their original position,
but the interface does not cool, and heat is not converted back to work.
Instead, more of the work is converted to heat
Unrestrained Expansion
• Another example of irreversibility is the unrestrained expansion of
a gas separated from a vacuum by a membrane. When the membrane is
ruptured, the gas fills the entire tank. The only way to restore the system
to its original state is to compress it to its initial volume, while transferring
heat from the gas until it reaches its initial temperature. From the
conservation of energy considerations, it can easily be shown that the
amount of heat transferred from the gas equals the amount of work done
on the gas by the surroundings. The restoration of the surroundings
involves conversion of this heat completely to work, which would violate
the second law. Therefore, unrestrained expansion of a gas is an
irreversible process.
Heat Transfer Through a Finite
Temperature Difference
• A third form of irreversibility familiar to us all is heat transfer
through afinite temperature difference. Consider a can of cold
soda left in a warm room Heat is transferred from the warmer
room air to the cooler soda. The only way this process can be
reversed and the soda restored to its original temperature is
to provide refrigeration, which requires some work input. At
the end of the reverse process, the soda will be`
Mixing of Two Different Substances
THE CARNOT CYCLE
• The Carnot cycle is a theoretical reversible cycle
commonly used to represent reversible heat engine or
reversible refrigerator/heat pump operation.
The efficiency of a heat-engine cycle greatly depends on
how the individual processes that make up the cycle
are executed. The net work, thus the cycle efficiency,
can be maximized by using processes that require the
least amount of work and deliver the most, that is, by
using reversible processes. Therefore, it is no surprise
that the most efficient cycles are reversible cycles,
that is, cycles that consist entirely of reversible
processes.
HEAT ENGINE (or REFRIGERATOR)
operating on the Carnot cycle
1 A reversible isothermal process in which heat is
transferred from (to) the high-temperature reservoir to
(from) the working fluid
2 A reversible adiabatic process in which the temperature
of the working fluid decreases from the high temperature
to the low temperature
3 A reversible isothermal process in which heat is
transferred from (to) the working fluid to (from) the low-
temperature reservoir
4 A reversible adiabatic process in which the temperature
of the working fluid increases from the low temperature to
the high temperature
Carnot Cycle
Reversible Isothermal Expansion Reversible Adiabatic Expansion
Reversible Isothermal Compression Reversible Adiabatic Compression
Carnot Cycles
QH TH
QL TL
Carnot Cycle(Heat Engine)
• The Carnot cycle efficiency for a heat engine
can now be expressed absolute temperatures
only
QL TL
t 1 1
QH TH
• The Carnot cycle efficiency is a function only
of the absolute temperatures of the thermal
reservoirs involved.
Example
Carnot Cycle
( Refrigerator)
• The Carnot cycle efficiency for a refrigerator
can now be expressed absolute temperatures
only
TL
COPref
TH TL
• The Carnot cycle efficiency is a function only
of the absolute temperatures of the thermal
reservoirs involved.
Carnot Cycle
( Heat Pump)
• The Carnot cycle efficiency for a refrigerator
can now be expressed absolute temperatures
only
TH
COPheatpump '
TH TL
• The Carnot cycle efficiency is a function only
of the absolute temperatures of the thermal
reservoirs involved.
Example
Propositions Regarding Carnot
Efficiency
• 1st Proposition:
It is impossible to construct an engine that
operates between two given reservoirs and is more
efficient than a reversible engine operating
between the same two reservoirs.
• 2nd Proposition:
All engines that operate on a Carnot cycle between
two given constant-temperature reservoirs have
the same efficiency.
Seatwork
• Differences in surface water and deep water
temperature can be utilized for power
generation. It is proposed to construct a cyclic
heat engine that will operate near Hawaii,
where the ocean temperature is 20°C near the
surface and 5°C at some depth. What is the
possible thermal efficiency of such a heat
engine?
Seatwork
We propose to heat a house in the winter with a heat pump.
The house is to be maintained at 20C at all times
When the ambient temperature outside drops to -10C,
the rate at which the heat is lost from the house is estimated to be 25 kW.
What is the minimum electrical power required to drive the heat pump?
Seatwork
• In a cryogenic experiment you need to keep a
container at -125°C although it gains 100 W
due to heat transfer. What is the smallest
motor you would need for a heat pump
absorbing heat from the container and
rejecting heat to the room at 20°C?
