5.1 Introduction to the Second Law of Thermodynamics
In the preceding chapters, we applied the conservation of energy principle or first law of
thermodynamics to open and closed systems. By now, it seems reasonable clear that in order for a
process to occur, it must obey the first law (Energy can neither be created nor destroyed!). But common
experience tells us that some processes proceed in certain directions. For instance, a hot cup of coffee
in a cooler room eventually cools off. The process satisfies the first law since the amount of energy lost
by the coffee is gained by the surrounding air. Now take the reverse process--a hot cup of coffee getting
hotter in a cooler room. We all know this could never happen, but doing so would not violate the first law
as long as the heat gained by the hot coffee is equal to the heat lost by the cool surroundings.
This is where the second law of thermodynamics comes into the picture! The second law
addresses the feasibility of processes and the directions they may or may not occur. The second law
also asserts that energy has quality as well as quantity. Preserving the quality of energy is a major
concern to engineers, and the second law provides the necessary means to determine the quality as well
as the degree of energy degradation during a process. The second law is also used to assess the
theoretical limits for the performance of commonly used engineering systems (e.g. refrigerators,
air-conditioning units, heaters etc ...)
5.2 Thermal Energy Reservoirs
In the development of the second law of thermodynamics, it is very useful to define a hypothetical
body with a relatively large thermal capacity that can supply or absorb finite amounts of heat without
undergoing any change in temperature (e.g. oceans, lakes, atmosphere and rivers). Such a body is
called a thermal energy reservoir , or simply reservoir. A two-phase system can be considered a
reservoir because it can absorb or release heat at constant temperature.
A reservoir that supplies energy in the form of heat is called a source, and one that absorbs
energy in the form of heat is called a sink.
5.3 Heat Engines
Consider the system illustrated below ...
Work
Heat
Water
The mechanical work done by the shaft is completely converted to internal energy and stored by
the water. This internal energy then leaves the water via heat transfer to the surroundings. We know,
from experience, that reverse process is impossible (i.e. supplying heat to the water form the
surroundings will make the shaft rotate). Thus, we may conclude that work may be converted to heat
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directly and completely, but converting heat to work requires the use of a special device called a heat
engine. Heat engines may vary considerably from one another, but share the following characteristics:
‚ They receive heat from a high temperature source.
‚ They convert part of this heat to work.
‚ They reject the remaining waste heat to a low-temperature sink.
‚ They operate on a cycle.
The work-producing device that best fits the definition of a heat engine is the steam power plant.
High Temp. Source
Q
in
Boiler
W
W
in
Pump
out
Turbine
Condenser
Q
out
Low Temp. Source
where: ‚ Qin = amount of heat supplied to steam in boiler from a high temperature source (furnace)
‚ Qout = amount of heat rejected from steam in condenser to a low temperature sink (river, etc...)
‚ Wout = amount of work delivered by steam as it expands in turbine
‚ Win = amount of work required to compress water to boiler pressure
Usually, a portion of the work output of a heat engine is consumed internally to maintain
continuous operation (e.g. work input to pump). The net work output of this power plant is simply the
difference between the total work output of the plant and the total work input, or ...
W net,out = W out − W in
(5.3.1)
The net work output of the power plant can also be obtained by treating the entire plant as a
closed system (no net mass flow of water into or out of the entire plant), and using the First law relation
for cycles to give ...
W net,out = Q in − Q out
(5.3.2)
The fraction of the heat input that is converted to net work output is a measure of the
performance of a heat engine and is called the thermal efficiency, ηth . Performance or efficiency, in
general, can be expressed in terms of the desired output and the required input as:
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(5.3.3)
For heat engines, the desired output is the net work output, and the required input is the amount
of heat supplied to the working fluid. Therefore, for heat engines ...
(5.3.4)
Typically, when dealing with heat engines, refrigerators, and heat pumps, we operate between a
high temperature medium at temperature TH and a low temperature reservoir at temperature TL. As a
result, we usually define heat transfer items as:
‚ QH = magnitude of heat transfer between cyclic device and high temperature medium at
temperature TH.
‚ QL = magnitude of heat transfer between cyclic device and low temperature medium at
temperature TL.
Therefore, for a heat engine, Eq. (5.3.4) is alternately expressed as:
(5.3.5)
The thermal efficiency of a heat engine is a measure of how efficiently a heat engine converts the
heat that it receives to work. Amazingly, most heat engine devices possess very poor thermal
efficiencies, with more than one-half of the thermal energy supplied to the working fluid ending up in
rivers, lakes, and/or the atmosphere.
Can we save Qout?
Unfortunately, heat rejection to a low temperature reservoir is a necessary part of the
thermodynamic cycle. Without it, the thermodynamic cycle cannot be completed and cyclic devices,
like steam power plants, cannot run continuously.
The Second Law of Thermodynamics: Kelvin-Planck Statement :
The Kelvin-Planck Statement asserts the requirement of Qout for thermodynamic cyclic devices.
Simply stated, the Kelvin-Planck statement reads:
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.
That is, a heat engine must exchange heat with a low temperature sink as well as a high
temperature source to keep operating.
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5.4 Refrigerators and Heat Pumps
We all know from experience that, in nature, heat flows in the direction of decreasing
temperature, i.e., from high temperature media to low temperature ones. The reverse process, however,
cannot occur by itself and requires the use of special devices called refrigerators. Refrigerators, like
heat engines are cyclic devices. The working fluid used in the refrigeration cycle is called a refrigerant.
The most frequently used refrigeration cycle is called the vapor-compression refrigeration cycle, shown
schematically below ...
High Temp. Reservoir
Q
H
Condenser
Expansion
Valve
Compressor
W
net,in
Evaporator
Q
L
Refrigerated Space
The refrigerant enters the compressor as a vapor and is compressed to the condenser pressure.
It leaves the compressor at a relatively high temperature and cools down and condenses as it flows
through the coils of the condenser by rejecting heat to the surrounding medium. It then enters a capillary
tube where its temperature and pressure drop drastically due to the throttling effect. The low temperature
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refrigerant then enters the evaporator, where it evaporates by absorbing heat from the refrigerated space.
The cycle is completed as the refrigerant leaves the evaporator and returns to the compressor.
The efficiency of a refrigerator is expressed in terms of the coefficient of performance (COP),
denoted by COPR. The COP of a refrigerator can be expressed as:
(5.4.1)
Note that the value of COPR can be greater than unity (and usually is for most refrigerator
devices)! That is, the amount of heat removed from the refrigerated space can be greater than the
amount of work input.
Another device that transfers heat from a low temperature medium to a high temperature one is
the heat pump. Refrigerators and heat pumps operate on the same thermodynamic cycle, but have
different objectives. The objective of a refrigerator is maintain the refrigerated space at a low
temperature. The objective of a heat pump is to maintain a heated space at a high temperature. The
coefficient of performance of a heat pump, COPHP, is defined as:
(5.4.2)
Note!
We all know that air-conditioning units are basically refrigerators whose refrigerated space is a
room or building. Did you know the same air-conditioning unit can operate as a heat pump in the winter
by installing it backwards!! In this mode, the air-conditioner absorbs heat from the refrigerated space
(outdoors) and rejects it to the heated space (your house!!). The performance of refrigerators and
air-conditioning units are often expressed in the U.S. in terms of the Energy Efficiency Rating (EER),
which is the amount of heat removed (in BTU's) for 1 watt-hour of electricity consumed. The relation
between EER and COP is:
EER = 3.412COP R
(5.4.3)
The Second Law of Thermodynamics: Clausius Statement:
Another classical statement of the Second Law of Thermodynamics, which is related to
refrigerators and heat pumps, is known as the Clausius Statement. Simply stated, it reads:
It is impossible to construct a device that operates in a cycle and produces no effect other than
the transfer of heat from a lower temperature body to a higher temperature body.
The Clausius Statement asserts that heat flows naturally in the direction of decreasing
temperature, but does not necessarily restrict the reverse from happening!! In fact, the statement is
open-ended and allows the possibility of work input to the refrigerator/heat pump device (into the
compressor !!) to accomplish heat flow from cold to hot temperature environments.
5.5 Perpetual-Motion Machines
Any device that violates the First/Second Laws of Thermodynamics is called a
perpetual-motion machine . Despite numerous attempts, no perpetual-motion machine is known to
have worked.
of
‚ Perpetual-motion machine of the first kind (PMM1): any device that violates the first law
thermodynamics
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second
‚ Perpetual-motion machine of the second kind (PMM2): any device that violates the
law of thermodynamics
5.6 Reversible and Irreversible Processes
A reversible process is defined as a process which can be reversed without leaving any trace
on its surroundings. That is, both the system and surroundings are returned to their initial states at the
end of the reverse process. Processes that are not reversible are called irreversible processes .
Reversible processes actually do not occur in nature. They are merely idealized processes, however,
some processes can come pretty close to satisfying the reversibility criterion!! Thus, analyses of real life
quasi-reversible processes can be facilitated by assuming they are in fact reversible. Engineers are
interested in reversible processes because work-producing devices (such as car engines and steam
turbines) deliver the most work and work consuming devices (such as compressors and pumps) require
the least work when reversible processes are used instead of irreversible processes.
Well, you might ask yourself, "What makes a process irreversible?" The answer is simple:
irreversibilities!!, and here are a list of some common irreversibilities ...
‚ electric resistances,
‚ inelastic deformation of solids,
‚ chemical reactions,
‚ friction (this is a big one),
‚ non quasi-equilibrium process (compression & expansions):
‚ heat transfer across a finite temperature difference (another big one)
Internally and Externally Reversible Processes:
A process is called internally reversible if no irreversibilities occur within the boundaries of the
system during the process. A process is called externally irreversible if no irreversibilities occur
outside the system boundaries during the process. A process is called totally reversible, or simply
reversible, if it involves no irreversibilities within the system or its surroundings.
5.7 Carnot Cycle
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.
Perhaps the best known reversible cycle is the Carnot cycle. The theoretical heat engine that operates
on the Carnot cycle is called the Carnot heat engine. The Carnot cycle is composed of four reversible
processes:
‚ Reversible isothermal expansion (process 1-2)
‚ Reversible adiabatic expansion (process 2-3)
‚ Reversible isothermal compression (process 3-4)
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‚ Reversible adiabatic compression (process 4-1)
P
Q
1
H
2
W
T =const.
H
net,out
4
3
T =const.
L
Q
L
v
The Reversed Carnot Cycle:
The Carnot heat-engine cycle described above is a totally reversible cycle. Therefore, all the
processes that comprise it can be reversed, in which case it becomes the Carnot refrigeration cycle.
This time, the cycle remains exactly the same, except that the directions of any heat or work interactions
are reversed.
5.8 The Carnot Principles
The following conclusions can be drawn from the Second Law and reversibilities concepts:
‚ The efficiency of an irreversible heat engine is always less than the efficiency of a reversible
one operating between the same two reservoirs.
‚ The efficiencies of all reversible heat engines operating between the same two reservoirs are
the same.
5.10 The Carnot Heat Engine
The thermal efficiency of any heat engine, reversible or irreversible, is given as:
(5.10.1)
The thermal efficiency of a Carnot engine, or any reversible heat engine, is:
(5.10.2)
where TL and TH are absolute temperatures. The thermal efficiencies of actual and reversible heat
engines operating between the same temperature limits compare as follows:
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if: ηth < ηth,rev (irreversible heat engine)
ηth = ηth,rev (reversible heat engine)
ηth > ηth,rev (impossible heat engine)
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5.11 The Carnot Refrigerator or Heat Pump
The coefficient of performance of any refrigerator or heat pump, reversible or irreversible, is given
by:
(5.11.1)
(5.11.2)
The COP relation for reversible refrigerators and heat pumps is:
(5.11.3)
(5.11.4)
These are the highest coefficients of performance that a refrigerator or a heat pump operating
between the temperature limits of TL and TH can have!! The coefficients of performance of actual and
reversible (such as Carnot) refrigerators operating between the same temperature limits can be
compared as follows:
if: COPR < COPR,rev (irreversible refrigerator)
COPR = COPR,rev (reversible refrigerator)
COPR > COPR,rev (impossible refrigerator)
... and, the same goes for heat pumps!!
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