Heat Engines

How heat is derived from fuels?

For example, we may consider the burning process for heptane,

C7H16, colorless liquid constituent of gasoline.

C7H16 + 11O2 → 7CO2 + 8H2O + 1.15x106 calories per 100g C7H16

Carbon dioxide and water are the only material products of the

reaction, and the energy liberated is in the form of heat.

The number at the right in the formula is the heat of combustion for

heptane. Every fuel has a tabulated value for this quantity.

The heat of combustion is the definite maximum amount of energy

available from a fuel, which cannot be exceeded.

1. The Energy Content of Fuels

1. The Energy Content of Fuels

Two basic purposes to obtain fossil fuels: to provide direct heating and

lighting , and to power heat engines

Figure 3.1 The general pathways by which we utilize energy from fossil fuels

2. The Mechanical Equivalent of Heat

Which one is larger?

1 Btu = 778 foot-pound

You can lifting a one-pound weight 778 feet into the air with the

energy released by the burning of only one match.

Capture the heat energy of the fuel and turn it into mechanical energy.

The possibility of easing human labor by utilizing heat sources has

been the driving force behind a long history of development of what

we now call heat engines.

Unit for heat energy: 1Btu

(raise the temperature of one pound of water by one degree Fahrenheit)

Unit for mechanical energy: 1 foot-pound

(raise one pound of water one foot higher)

3. The Thermodynamic of Heat Engines

A heat engine is any device that can take energy from a warm source and

convert a fraction of this heat energy to mechanical energy.

Figure 3.2 A thermodynamic

diagram of a heat engine operating

between a heat source and heat sink

at a lower temperature. The work

output must equal the difference

between the heat energy extracted

from the source and that rejected to

the sink – the Principle of Energy

Conservation.

Not all of the heat energy taken from the source is being used to performed

useful work. Some fraction of the heat energy must always be rejected, at a

temperature cooler than that of the warm source, to the environment.

– The second law of thermodynamics

Kelvin statement:

It is impossible to convert heat completely into works in a cyclic process.

Clausius statement:

Heat generally cannot flow spontaneously from a material at lower

temperature to a material at higher temperature.

In a system, a process that occurs will tend to increase the total

entropy of the universe.

Efficiency = work done

energy put into the system < 100%

Efficiency = work done

energy put into the system

Efficiency = Qhot - Qcold

Qhot

= (1 - ) x 100% Qcold

Qhot

For an ideal engine, the ratio of two energy terms is identical to the ratio of

two temperature terms:

Qcold / Qhot = Tcold / Thot

where the temperatures are given on the absolute (Kelvin) scale.

Tcold Efficiency = (1 - ) x 100% Thot

It is remarkable that this efficiency (Carnot) depends only on the

temperatures of the two reservoirs between which the heat engine operates.

Carnot

A Carnot cycle taking place between a

hot reservoir at temperature TH and a

cold reservoir at temperature TC.

A generalized thermodynamic cycle

Tcold Efficiency = (1 - ) x 100% Thot

Example:

For a coal-fire electric power plant, Thot (the boiler temperature) would be 825 K,

and Tcold (the cooling tower) would be about 300 K. This leads to

Efficiency = (1 – 300 / 825) x 100% = (1 – 0.36) x 100% = 64%

• In this case, 36% of the heat energy from the energy of the fuel must be

wasted by rejecting it through the cooling tower to the surrounding

atmosphere.

• To make the efficiency as high as possible, it would be desirable to

increase Thot and decrease Tcold.

• The limit on Thot is imposed by the materials from which the boilers can be

constructed and the limit on Tcold is imposed by the availability in nature of

large sinks at sufficiently low temperature.

4. Generation of Electricity

In 1831, in London, Michael Faraday (1791-1876) discovered electromagnetic

induction – one of the greatest discoveries of all time.

Electromagnetic induction is the production of

voltage across a conductor situated in a changing

magnetic field or a conductor moving through a

stationary magnetic field.

The discovery made the generation and transmission of electricity possible,

and quickly lead to the invention of electric generators.

"This is all very interesting, but of what possible use are these toys?"

"I cannot say what use they may be, but I can confidently predict that

one day you will be able to tax them."

“ Of what use is a newborn baby? ”

Figure 3.4 An elementary

alternating current generator. A

loop of wire is forced to rotate in

a magnetic field. The induced

alternating current enters the

external circuit through contacts

(carbon brushes) that rub against

rotating metal rings, called slip

rings, attached to the coil. The

current generated, I, reverses in

direction as the coil rotates.

right hand rule & left hand rule

The current induced in the coils according to the Faraday law interacts

with the magnetic field to resist the motion of the coils through the field.

Therefore it takes energy from some external source to force the rotation.

Figure 3.3 A diagram of a

fuel-burning electric power

plant. Here a river provides

cooling water to the

condenser, but lake water or

a cooling tower could serve

the same purpose.

Most electric power plants have the rotating coils of the generator mechanically

connected to steam turbines or to water-driven hydroelectric turbines at large

dams. The main components of a typical electric power plant are shown in the

figure below.

Figure 3.5 Typical efficiency of an electric power plant for converting

chemical energy in the fuel into electric energy. The best new plants

now achieve nearly 40%.

5. Electric Power Transmission

• In order for electric energy to be useful to society, it must be

transported in some way from the power plants to factories or

residences.

• The first electric power system was developed by Thomas

Edison in New York in 1882, using direct current (DC).

• Alternating current (AC) offered greater flexibility in changing the

voltage at different points in the system with transformers.

• Raising the voltage continues to be the main way to reduce

transmission losses. (The loss is proportional to I2·R.)

Transmission and distribution losses in the USA were estimated at 7.2% in 1995 .

Diagram of an electrical system

The system of generating stations, substations and transmission lines is

called the electric power grid. Most of the electric power companies in

North America are integrated into a single power grid (3000 power plants,

200,000 miles of high-voltage transmission lines) for reasons of economy,

availability of backup power for emergencies, and ability to trade energy.

Wireless Transmission of Electricity?!

6. Practical Heat Engines

The 1698 Savery

Engine – the first

commercially-useful

steam engine: built

by Thomas Savery.

Early Watt pumping

engine (James Watt,

1770s)

Heat engines have steadily improved since they were first invented 300 years ago.

First compound Steam

Turbine, built by Charles

Parsons in 1887 – basis

for most of our electricity

generation now.

5.1 Steam Engines

A steam engine is a heat engine that performs mechanical work using

steam as its working fluid.

A locomotive powered by the force of

steam against pistons. The motion of

the pistons is coupled by connecting

rods directly to the drive wheels.

Principle of operation for a steam engine:

• When water is boiled to steam at

atmosphere pressure, its volume

expands about a thousand times.

• If the steam is confined, pressure

builds up and the steam tries to

expand with great force.

• This force can exerted against a

piston or it can work against the

blades of a turbine.

A rotor of a modern steam turbine,

used in a power plant

• When steam at high pressure is admitted

to one side of a turbine, it will force the

blade assembly to rotate.

• This rotation is achieved most effectively

if the exhaust side of the turbine is

maintained at low pressure.

• The low pressure condition is assured by

the presence of a condenser, typically a

chamber into which the exhaust steam is

admitted and kept cool by a flow of water

from a river, lake, or other source.

• The mechanical energy of the rotating

turbine can be coupled to other

machinery, often to an electric generator.

Working Mechanism for Steam Turbine

Steam engines belong to the broad class of external combustion heat

engine.

In engine of this type, the fuel is burned outside of the pressurized part of

the engine, at a relatively low temperature, at atmospheric pressure, and

in the presence of an abundance of air.

• Low emission of carbon monoxide and nitrogen oxides

• Emission of sulfur oxides and particulates depends on the fuel being

burned.

5.2 Gasoline Engines

Figure 3.9 The four strokes of a four

spark-ignited internal combustion engine:

(a) compression, (b) combustion,

(c) exhaust, and (d) fuel-air intake.

• The heat engine we now have in almost

all of our motor vehicles are internal

combustion engines.

• Gasoline is vaporized and mixed with air

to form a combustible mixture inside a

closed chamber.

• The mixture is compressed to about 6 to

10 times atmospheric pressure, then

ignited with an electric spark.

• On ignition, the fuel explodes, forming

hot gases (CO2, H2O, N2 …).

• The resulting hot gases (1000 oC)

expand with great force against the

piston, causing the crankshaft to rotate.

• About 25% of the chemical energy in the

fuel can be converted to mechanical

energy in a modern gasoline engine.

5.3 Diesel Engines

Figure 3.10 Cutaway drawing of a

diesel engine. Ignition is accomplished

by the high temperature produced by

the compressed of air.

The diesel engine is an internal combustion

engine similar to the gasoline engine.

Difference: Diesel engine does not use

electric spark ignition and it does not mix the

fuel and air before admitting them to the

combustion chamber.

• During the compression stroke, the diesel

combustion chamber contains only air.

• The pressure can reach as high as 15 atm and

the temperature of the compressed air has been

increased to the ignition point for a fuel-air mix.

• A short burst of fuel is injected into the chamber.

• The fuel mixes with the hot air and immediately

ignites without the help of an electric spark.

Advantage:

• The combustion temperature of diesel engine is higher than in a

spark-ignited gasoline engine, producing a higher thermodynamic

efficiency (> 30%).

• Diesel fuel has about 10% more Btu per gallon than gasoline.

• Low CO emission due to an excess of air (and oxygen) in the

combustion chamber

Disadvantage:

• Greater noisiness, initial cost, and weight

• Harder starting in cold weather

• Characteristic odor and visible smoke

• Greater emission of nitrogen oxides

5.4 Gas Turbines Diagram of a gas turbine engine

•A gas turbine, also called a combustion turbine, is a rotary engine that extracts

energy from a flow of combustion gas. It has an upstream compressor coupled to a

downstream turbine, and a combustion chamber in-between.

•Energy is added to the gas stream in the combustor, where air is mixed with fuel

and ignited. Combustion increases the temperature and volume of the gas flow. This

is directed through a nozzle over the turbine's blades, spinning the turbine and

powering the compressor.

•Energy is extracted in the form of shaft power, compressed air and thrust, in any

combination, and used to power aircraft, trains, ships, generators, and even tanks.

A continuously

running gasoline

engine

Diagram of a gas turbine engine

different design for jet plane and electricity generator

For electricity generator: the turbine is designed to give larger fraction of its

power to the rotating shaft which is connected to the shaft of the generator.

For aircraft jet engine: the shaft needs only enough power for the compressor

fan, the rest of the energy going into kinetic energy of the exhaust gases.

Advantage: light, inexpensive, respond well to sudden power demand

Disadvantage: relative low efficiency (20 to 30%)

7. Heat Pumps

Figure 3.11 A thermodynamic diagram of a heat pump.

A work input, W, is required to transfer an amount of

energy Qcold, out of a cold reservoir and a larger amount,

Qhot, into a hot reservoir. Because energy is conserved,

Qhot must equal W + Qcold.

The second law of thermodynamics

(Clausius statement)

Heat generally cannot flow spontaneously

from a material at lower temperature to a

material at higher temperature.

Can we remove energy from a cold

place and deliver it to a warmer place ?

Can we run the heat engine backward?

Heat pump: a device using

energy input in the form of

work to cause the transfer of

heat energy from the low T

to the another reservoir with

higher T.

The Coefficient of Performance (COP) is used to measure the effectiveness

of the heat pump.

COP = Qh/W = Qh/(Qh – Qc) = Th/(Th – Tc)

Calculate the ideal COP for an air-to-air heat pump used to maintain the

temperature of a house at 21oC when the outside temperature is -1oC.

Solution

Th = 21oC = 294 K

Tc = -1oC = 272 K

COP = Th/ (Th – Tc) = 294K/(294K – 272K) = 13.3

Thus, for each watt of power used to drive this heat pump, 13.3 watts are

delivered to the hot reservoir (the interior of the house), and 12.3 watts

are extracted from the cold reservoir (the outside the house). In practice,

the COP for such a situation would be much less favorable (in the range

of 2-6).

Example:

COP = Qh/W = Qh/(Qh – Qc) = Th/(Th – Tc)

The COP will diminish if the outside temperature drops. So electrically driven

air-to-air heat pumps are most useful in moderate climate (> -10oC). In

addition to the air-to-air heat pumps, it is common to use the ground at

several feet of depth, or surface water such as a river for the cold reservoir.

Figure 3.12 An electrically driven heat pump using

Freon as a working fluid.

Freon gas is

compressed by a

compressor to

raise its T and P.

The warm gas flows

through a heat

exchanger where it

is cooled by a flow

of room T air and

condensed to a

liquid, thus giving

up heat to the room.

On passage through

an expansion valve

into a region of

lower pressure, the

liquid expands into a

gas, becoming very

much colder.

The extremely cold gas

flows through a second

heat exchanger where it

is warmed to the outside

air T, thus extracting heat

from the outside air.

adiabatic

expansion

8. Cogeneration (废热发电，热电联产)

Cogeneration (also combined heat and power, CHP) is the use of a

heat engine to simultaneously generate both electricity and useful heat.

• The operation of a heat engine for any purpose is necessarily

accompanied by the rejection of heat energy, often in large amounts.

• The waste heat is generally dissipated into the atmosphere or an

adjacent body of water with possible negative environmental effects.

• A simple example of beneficial use of waste heat energy is using the

heater in an automobile.

• A cogeneration plant uses the rejected heat energy from electricity

generator for space heating in cities.

• A cogeneration plant is usually a small, decentralized electric generating

plants near the point of use, even right in the middle of a university

campus.

Efficiency = work done + Qcold

energy put into the system

Figure 3.13 A small cogeneration plant that uses the combustion of natural gas to

drive a gas turbine coupled to an electric generator. The hot exhaust gases boil water

to steam for use in space heating.

Efficiency of a new

coal-fired electric

power plant – 38%

Overall efficiency

of a cogeneration

can reach 70%.