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PHYX 1020
ENERGY
CHAPTER3 HEAT ENGINES
CHAPTER 3
HEAT ENGINES
Stephenson’s
Rocket, 1829
2002
USU 1360
Modern Industrial
Diesel Engine
Industrial
Gas Turbine
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CHAPTER3 HEAT ENGINES
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Heat Energy (Recap)
• Heat or internal energy is a consequence of the collective kinetic
(motion) energy of the atoms/molecules in the substance.
• An index of the average speed of the particles is the TEMPERATURE of
the substance
• Temperature is described as a measure of the “hotness” or “coldness” of
an object
• The amount of heat energy depends on the mass (number of particles)
and the temperature
• There is an absolute zero on the Kelvin temperature scale, all material
above 0K has heat (internal) energy - even what we term “cold” material
• Heat energy results from the conversion of many other forms of energy,
and is commonly the last form of energy in chains conversions as well as
partial conversions along the chain.
• In order to be useful heat has to be transported from where it is generated
to where it is needed
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Heat Transport
• There are three method of transporting heat energy
– Conduction
– Convection
– Radiation
• Conduction
– Collisions between adjacent particles result in an increase in heat energy at a
distance from a heat source
• E.g. A poker in a fire
•
Transfer of heat through the base of a saucepan from an energy source
•
Transfer of heat from a furnace to a boiler
• Convection (Passive or Forced)
– Transfer of heat energy by physical movement of material in bulk
• E.g. Distribution of heat energy in water from the base of a saucepan (passive)
•
Distribution of hot air in a domestic heating system (forced)
•
Cooling of a computer by a fan (forced)
• Radiation
– Transfer of heat energy by generation of electromagnetic waves by any
substance above absolute zero temperature
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• E.g. Transfer of heat energy from the sun to the earth
•
Transfer of heat energy from an electric fire to a person
•
Transfer of heat energy from the atmosphere to the Universe
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Equivalence of Mechanical and Heat
(Internal) Energy - Rumford
• An early observation of the conversion
of mechanical work into heat energy
occurred during the boring of cannons
by Count Rumford (~1800)
– The water in the barrel used to keep the
cannon barrel cool boiled away and had
to be regularly replenished
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– The work done was the force of the tool
in the direction of the metal cut times the
distance traveled.
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Equivalence of Mechanical and Heat
(Internal) Energy - Joule
• This was quantified in experiments by
Joule in 1843 which compared the rise
in temperature of a mass of water with
a measured amount of work performed
on the water
– Led to the following equivalencies:
• 1kcal (1000 cals)
• 1 Btu
4186 Joules
777.9 ft lb
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Joule’s Apparatus for Mechanical Equivalent of Heat
Loss of gravitational
potential energy of weights
equals the gain in heat
energy of water.
Work is done on the water
by the force exerted by the
paddles multiplied by the
distance they move in the
water.
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Conversion of Heat Energy to
Mechanical Work
• This led to the understanding of how
the reverse could occur i.e.:
– Conversion of heat (internal) energy to
mechanical energy
• The technology to do this results in a
HEAT ENGINE
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What is a Heat Engine?
• A heat engine is the generic name given to devices
which convert heat (internal) energy into
mechanical energy.
• In most practical devices heat is used to boil a liquid
and increase the pressure of a gas that is then
arranged to provide a force on a surface which can
be used to perform mechanical work
– (force x distance in direction of the force)
• Practical devices are technically very complex, but
for our purposes heat engines will be discussed in
simplified terms of the thermodynamic diagram
shown on the next page:
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Schematic Diagram of Heat Engine
Heat flow from
hot reservoir
Heat flow to
cold reservoir
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Energy Content of Fuels (1)
• Energy stored in the fuels is released in the
form of heat (internal) energy as a result of
causing the fuel to undergo an
EXOTHERMIC chemical reaction
– Since oxygen is plentiful in the air and is a
reactive element the exothermic reaction of choice
is oxidation of the fuel.
– That is causing the fuel molecules to combine
with oxygen, form other compounds and release
heat.
– The rate of burning determines the rate of heat
energy generation - i.e. the power produced
– This can be increased by extra oxygen - e.g. in
rocket motors, supercharged internal combustion
engines
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Energy Content of Fuels (2)
• Carbon
C + O2
CO2 + 33MJ/kg
• Hydrogen 2H2 + O2
• Heptane C7H16 + 11O2
48.1MJ/kg
2H2O + 142MJ/kg
7CO2 + 8H2O +
• The energy released is also called the heat of
combustion.
• Most fuel oxidation reactions proceed very slowly at
normal temperatures so the fuel is arranged so that it
is heated by some of the heat of combustion. In this
arrangement the process known as burning.
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Burning (1)
• Burning is the fast oxidation that is caused to
happen when fuels are used to produce heat
energy
• Some of the heat energy produced is use to
maintain the fuel at a high enough temperature
that the reaction with oxygen proceeds rapidly.
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Burning (2)
• In order for the rapid reaction speed to occur the
fuel must first be raised to a high temperature
– E.g. using an already burning fuel (e.g. a match) to light
a candle
– Initiating the burning of the gasoline in an internal
combustion engine by the arc at the spark plug
• After the initiating the rapid reaction, it then
proceeds without further assistance because the
high temperature is maintained by part of the heat
of combustion.
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Burning (3)
• Fuels differ in the temperature needed to
cause the rapid oxidation reaction to
proceed
– E.g the charcoal lighting fuel can be induced to
burn by a match
– Whereas the charcoal needs to be raised to a
much higher temperature for burning to
proceed
– Gasoline ignites at a relatively low temperature
– The temperature for ignition to occur is called
the FLASHPOINT
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Thermodynamics (1)
• The Science of Thermodynamics evolved in
the 19th century as the development of the
steam engine progressed.
• It is the study of the physics of the
processes which allow us to convert the heat
(internal) energy of fluids into mechanical
energy.
• Observation shows us that heat engines do
not totally convert the heat energy to
mechanical energy.
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Thermodynamics (2)
• There is always some heat rejected from the
engine.
– E.g The water surrounding a car engine gets hot
– The steam turbines in a power station reject heat energy
which must be dissipated in lakes, rivers or cooling
towers.
• This leads us to be interested in the efficiency of
heat engines
– How much of the heat energy is converted to
mechanical energy?
– What factors determine the efficiency?
• In order to demonstrate and calculate heat engine
efficiencies, we must first further consider
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temperatures.
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Temperature (1)
• The temperature of a substance is an index which is
related to the average speed of the particles making
up the substance.
• The actual numbers used depend on the
temperature scale used
• Certain points on the scale are defined because they
come from well defined and reproducible
temperatures
– E.g. Boiling water, melting ice
• Commonly used scales in everyday life are:
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– Fahrenheit Boiling 212°F; Melting ice 32°F 180 steps of
1 degree
– Celsius (Centigrade) Boiling 100°C; Melting ice 0°C
100 steps of 1 degree
– They are related by : °C = 5/9 (°F-32)
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Temperature (2)
• The problem is that commonly used scales
allow negative temperatures which is
inconsistent with their representation of the
average speed (a positive scalar quantity) of
the particles.
• In thermodynamic calculations we get
around this by defining another scale
– The Kelvin scale K
– One K degree is the same step as one C degree
– Experimentally it has been found that the
average speed is zero at -273°C
– This is defined as 0K
– Thus K = °C + 273 or °C = K - 273
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Second Law of Thermodynamics
• This is a very important law connected with
thermal energy conversion
– It rules out perpetual motion machines
• It is stated in various ways, but in relation to heat
engines:
– It is not possible to extract heat from a hot reservoir and
convert it to mechanical energy with rejecting heat
energy to a cooler reservoir.
• The complement of this is that it is not possible for
heat to be transferred from a cooler reservoir to a
hotter reservoir without the performance of work
on the system.
• We can apply this to and ideal heat engine (next)
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Schematic Heat Engine -Efficiency
•For a heat engine we can define:
–Efficiency = mechanical work done / heat energy supplied
•Eff. = W / Qhot
•Or Eff. = (Qhot - Qcold) / Qhot
• For a reversible heat
engine:
•Qhot / Qcold = Thot / Tcold
•Where T in °K
•(Carnot 1824)
Eff. = (1-Qcold / Qhot)
Thus Eff. = (1-Tcold/Thot)
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Efficiencies of Practical Heat
Engines
• We will consider some practical heat engines and
calculate their maximum thermodynamic efficiencies.
( See book for more details.)
• Steps needed
– Eff = (1-Tc/Th) , Tc and Th are temperatures of the cold
and hot reservoirs respectivly
– Need to compute Tc and Th on in Kelvin scale
– Substitute in Eff formula to find maximum engine efficiency
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– Note that inspection of the formula tells us the if Th >> Tc,
the efficiency will be higher.
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Heat Engines - Steam Engine
– Steam engine
• Piston and cylinder (train engines 1830’s to
1950’s)
– Th = 250°C = (250 + 273) K = 523K;
– Tc = 25°C = (25 + 273) K = 298K
– Eff = (1-Tc/Th) = (1-298/523) = 0.43 or 43%
• Steam turbine (ships, fossil fuelled and
nuclear power stations)
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– Th = 550°C = (550 + 273)K = 823K;
– Tc = 25°C = (25 + 273)K = 298K
– Eff = (1-Tc/Th) = (1-298/823) = 0.64 or 64%
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Heat Engines - Internal Combustion
– Internal combustion engines
• Gasoline engine (cars, private airplanes,
small garden appliances)
– Th = 700°C = (700 + 273) K = 973K;
– Tc = 25°C = (25 + 273) K = 298K
– Eff = (1-Tc/Th) = (1-298/973) = 0.69 or 69%
• Diesel engine(large trucks, ships,
locomotives, farm appliances)
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– Th = 950°C = (950 + 273) K = 1223K;
– Tc = 25°C = (25 + 273) K = 298K
– Eff = (1-Tc/Th) = (1-298/1223) = 0.76 or 76%
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Heat Engine - Gas Turbine
– Gas turbine (Passenger and defense
airplanes, electrical power stations)
• Th = 1500°C = (1500 + 273) K = 1773K;
• Tc = 25°C = (25 + 273) K = 298K
• Eff = (1-Tc/Th) = (1-298/1773) = 0.83 or 83%
• If Tc = -40°C (stratosphere)
• Eff = (1-Tc/Th) = (1-233/1773) = 0.87 or 87%
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Heat Pumps
• Recall that in discussing the second law of
thermodynamics we said that heat could be made to
flow from a cold reservoir to a hot reservoir if work
is done on the system.
• This is the basis of the heat pump used for space
heating, and can be represented by a thermodynamic
diagram similar to that for a heat engine, but with the
heat and energy flows reversed.
• As drawn more energy is coming from the reservoir
than from the external energy source
• This means that more energy is being delivered than
supplied by the external source W
• The conditions for this are described by the
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Coefficient of Performance (COP)
COP 
HeatEnergy Delivered
Work Done
Qh
Qh
COP 

W Qh Qc
1
COP 
(1 Qc Qh )
COP 
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1
Th

(1 Tc Th ) Th Tc
Carnot’s principle
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Heat Pumps (2)
• Examples of calculation of COP for space
heating
– Moderate climate
• Inside temperature = 22°C (72°F) = (22 + 273)K = 295K
• Outside temperature = 0°C (32°F) = (0 + 273)K = 273K
• COP = 295 / (295 - 273) = 295 / 22 = 13.4
– Cold climate
• Inside temperature = 22°C (72°F) = (22 + 273)K = 295K
• Outside temperature = -30°C (-22°F)=(-30+273)K = 243K
• COP = 295 / (295 - 243) = 295 / 52 = 5.7
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Heat Pumps (3)
• Thus we see two important results
– The COP is much higher in moderate climates
than in cold climates
– It is predicted that for every watt of energy
supplied to the heat pump 5 - 13 watts of heat
energy is supplied to the building.
• In practice these COP’s cannot be achieved,
but figures of 2-6 are possible in moderate
climates
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Heat Pumps(3)
The heat pump works on the same
principle as the refrigerator.
The equivalent of the heat exchanger on
the back of the refrigerator supplies
energy to the building.
In practice heat
pumps are complex
and quite costly
items
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Electricity (1)
• Electricity is the name given to a form of energy that
arises from the separation of positive and negative
charge in devices.
• The measure of the energy available for conversion
is determined by the voltage of an object which is the
work needed to bring a unit charge of the same sign
as the voltage from the place the voltage is measured
with respect to to the charged object.
– Note the force between like charges is repulsion, between
unlike charges it is attraction. It is called the COULOMB
force.
• The concept of work being done by moving the
charge due to the Coulomb force leads to the concept
of electric current which is charge moving at a steady
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Electricity (2)
• Electric current results from connecting a LOAD
between the charged object and the point its voltage is
measured with respect to.
• The power delivered to the load is P = I x V where I
is the current through the load and V the voltage
across it.
– Note the same power can result from a high current and
small voltage or vice-versa
• The electric current produces a magnetic field which
results in forces on certain materials (e.g. iron) and on
the magnetic field produced by other currents.
• If the current is not constant some of the electrical
energy is converted to electromagnetic wave energy.
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Generation of Electrical Energy(1)
• One of the most convenient forms of
energy for myriad uses in industry,
business and the home is electrical
energy.
• Most of the electricity produced in this
country uses a heat engine to provide
the mechanical energy to drive an
electric generator.
– This is only one of several ways to generate
electrical energy
Michael
Faraday
1791 - 1867
• The electric generator relies on a
principle of physics discovered by the
British physicist Michael Faraday in
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1831.
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Generation of Electrical Energy(2)
• The principle is called
– Electromagnetic Induction
– If there is relative motion between a conductor and a
– magnetic field a voltage is induced in the conductor and
– it can drive an electric current if the conductor is
connected to an external circuit.
• Thus moving a wire in the presence of a magnetic
field can be used to generate electrical energy
– The voltage (electrical energy) induced depends on:
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• Strength of magnetic field
• Speed of motion of the conductor
• Length of conductor
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Generation of Electrical Energy(2)
• Since man-made strong magnetic fields
are confined to fairly small volumes,
the motion of the wire must also be
constrained to be within that volume
– This is achieved by using a rotating
system
• The length of the wire is made large by
winding it into a coil
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• The high speed motion relative to the
magnetic speed is controlled by the rotation
speed of the coil
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Generation of Electrical Energy(2)
• The schematic diagram
shows why alternating
current (AC) is produced
by a generator
• Direct current (DC)
generation is possible
using a different
arrangement
• When use of electrical
energy became
widespread, there was a
battle between proponents
of AC and DC
• AC proponents won for
reasons to be discussed
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later
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Generation of Electrical Energy(4)
Steam-Driven Turbo generator
High pressure
turbine
Electrical
Generator
Coal in:
10,572 tons/day
Steam produced:
3650 psi
1,000°F
8x106 lb/hour
Medium
pressure
turbine
Low pressure
turbine
Electrical
Generator
Electrical power:
1150 MW
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Efficiency:
39.3%
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Power Stations
W
Qh
Qc
• Prime source of energy in - fossil / nuclear fuel
• Heat engine energy flows - Qh, Qc, W
2002 • Generation of electricity - electromagnetic induction in generator
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Distribution of Electrical Energy
• Electric power = Current x Voltage
–
P= IxV
• Power loss due to resistance of wires
– Loss = I2 Rwires
• Desirable to keep current in long
wires as low as possible
• Thus need to use high voltage for
long runs from power station to users
• AC best for this because of ease in
changing voltage up/down using a
transformer.
• Typical distribution voltages
–
–
–
–
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Power station
Long distance
City distribution
Internal to buildings
25,000 V
345,000 V
440 V
120 V
• Distribution grid facilitates load
sharing
Distribution of
Electricity
Cables and Pylons
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Utilization of Electrical Energy (1)
• Electricity is a very convenient form of energy
– Delivered compactly and continuously by wires
– Easily controlled by switches
– Technology well developed to convert it to heat
energy, mechanical energy, electromagnetic wave
energy and light energy
– Very low pollution when it is converted to other
forms of energy
• Some motors can produce ozone if sparking occurs
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– Conversion to thermal energy for space heating is
close to 100% efficient
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Utilization of Electrical Energy (2)
• Electricity has some drawbacks
– The possibility of electrocution
– Excessive currents can cause wires to
overheat and melt or burn insulation
– Power stations can emit large quantities
of pollutants into the atmosphere
– Overhead wire distribution is unsightly
– Storage is bulky using batteries
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Utilization of Electrical Energy (3)
• Future may involve fuels cells
– Local generation at house level
– Will need the supply of hydrogen for the
fuel cells to be worked out
– Could provide energy for transportation
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Cogeneration
• We have seen earlier that heat engines must reject
heat energy at a lower temperature than the input
energy
• The utilization of some or all of this rejected energy
is known as COGENERATION
– E.g. a modern coal fired power station uses heat engines
that are 38% efficient
– Thus 62% of the input heat energy is available for other
purposes which need heat energy at a lower temperature.
– For example space heating from heat energy rejected from
power stations.
• We all make use of cogeneration in our car heaters
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– These devices extract heat rejected by the internal
combustion engine and use it for space heating in the car.
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Learning Objectives(1)
• Understand what is meant by heat (or internal) energy of material
• Understand that any material above absolute zero temperature has heat
energy
• Know the three methods of transporting heat energy
• Be aware of the early work in showing that the performance of work
could result in conversion to heat energy. (Rumford, Joule)
• Know what is meant in general by the term “Heat Engine”
• Know that the chemical energy in fuels can be used to produce heat
energy to be used in heat engines through exothermic oxidation
reactions
• Understand that to extract heat rapidly the oxidation process must be
speeded up in the process called “Burning”
• Know what is meant by the term “Thermodynamics”
• Know what property of material is represented by its temperature
• Be aware of different temperature scales.
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Learning Objectives(2)
• Know what is meant by the absolute or Kelvin temperature scale and
how to convert between the Kelvin and Celsius scales
• Know a statement of the second law of thermodynamics as it relates to
heat engines.
• Understand that the second law of thermodynamics implies that no
heat engine can be 100% efficient
• Know the simplified diagram of a heat engine and how to use it to
write down its efficiency in terms of heat in and work and heat out
• Understand how to apply Carnot’s principle to calculate the efficiency
of a heat engine in terms of the temperatures of the hot and cold
reservoirs attached to the engine
• Know some examples of practical heat engines
• Know what is meant by a heat pump
• Know how the temperatures of the hot and cold reservoirs attached to a
heat pump determine its maximum coefficient of performance.
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Learning Objectives(3)
• Know the difference between voltage and electrical current
• Know how the electrical power in a load is related to the voltage
across the load and the current flowing through it
• Be aware of the production of electrical energy from mechanical
energy by electromagnetic induction discovered by Michael Faraday
• Understand the principle of the alternator as a practical means of
converting mechanical energy to electrical energy.
• Know the principle components of a fossil fuelled power station
• Understand why the transmission of electricity over long distances is
best accomplished at high voltages
• Be familiar with the approximate voltage levels for transmission of
electrical power in different parts of the transmission circuit.
• Be aware of the relatively simple means of changing alternating
voltage levels by the device called a transformer
• Understand what is meant by the term “cogeneration” and some
examples of cogeneration
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