CHAPTER 3 HEAT ENGINES

1. CHAPTER 3HEAT ENGINES Stephenson’s Rocket, 1829 Modern Industrial Diesel Engine Industrial Gas Turbine

2. 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

3. 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 • 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

4. 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 • The work done was the force of the tool in the direction of the metal cut times the distance traveled.

5. 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) 4186 Joules • 1 Btu 777.9 ft lb

6. 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.

7. 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

8. 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:

9. Schematic Diagram of Heat Engine Heat flow from hot reservoir Heat flow to cold reservoir

10. 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

11. Energy Content of Fuels (2) • Carbon C + O2 CO2 + 33MJ/kg • Hydrogen 2H2 + O2 2H2O + 142MJ/kg • Heptane C7H16 + 11O2 7CO2 + 8H2O + 48.1MJ/kg • 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.

12. 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.

13. 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.

14. 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

15. 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.

16. 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 temperatures.

17. 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: • 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)

18. 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

19. 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)

20. 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)

21. 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 • Note that inspection of the formula tells us the if Th >> Tc, the efficiency will be higher.

22. 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) • 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%

23. 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) • 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%

24. 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%

25. 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 • Coefficient of Performance (COP)

26. Coefficient of Performance (COP) Carnot’s principle

27. 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

28. 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

29. In practice heat pumps are complex and quite costly items 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.

30. 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 speed in conductors (solid, liquid or gas (plasma))

31. 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.

32. Michael Faraday 1791 - 1867 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 • The electric generator relies on a principle of physics discovered by the British physicist Michael Faraday in 1831.

33. 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: • Strength of magnetic field • Speed of motion of the conductor • Length of conductor

34. 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 • The high speed motion relative to the magnetic speed is controlled by the rotation speed of the coil

35. 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 later

36. Medium pressure turbine High pressure turbine Electrical Generator Low pressure turbine Electrical Generator Generation of Electrical Energy(4) Steam-Driven Turbo generator Coal in: 10,572 tons/day Steam produced: 3650 psi 1,000°F 8x106 lb/hour Electrical power: 1150 MW Efficiency: 39.3%

37. Power Stations W Qh • Prime source of energy in - fossil / nuclear fuel • Heat engine energy flows - Qh, Qc, W • Generation of electricity - electromagnetic induction in generator Qc

38. Distribution of Electrical Energy • Electric power = Current x Voltage • P = I x V • 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 • Power station 25,000 V • Long distance 345,000 V • City distribution 440 V • Internal to buildings 120 V • Distribution grid facilitates load sharing Distribution of Electricity Cables and Pylons

39. 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 • Conversion to thermal energy for space heating is close to 100% efficient

40. 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

41. 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

42. 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 • These devices extract heat rejected by the internal combustion engine and use it for space heating in the car.

43. 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.

44. 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.

45. 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