Unit 2 Physics Summary PDF

UNIT 2 – PHYSICS (SUMMARY) PART 1 (INTRODUCTION & MATTER) Matter refers to everything which occupies space, and has mass which exists in one of three physical states, solid, liquid and gaseous. The total mass of the universe...

UNIT 2 – PHYSICS (SUMMARY) PART 1 (INTRODUCTION & MATTER) Matter refers to everything which occupies space, and has mass which exists in one of three physical states, solid, liquid and gaseous. The total mass of the universe is conserved; this meaning it cannot be created or destroyed, only changed from one form to another. A chemical element is a substance that cannot be broken down by chemical means. Although elements aren't changed by chemical reactions, new elements may be formed by nuclear reactions. Matter itself is made up of small particles. The simplest forms of matter are the elements, whose constituent particles are called atoms. Atoms are largely spaced with a relatively dense nucleus made up of elementary particles, protons and neutrons, and one or more shells of electrons at certain fixed distances. Imagine the full stop at the end of this sentence. It is probably about 0.5 mm in diameter. If that represents the nucleus, then the electrons in the first shell would be about 50 meters away. Protons are considered to have positive charge, whilst electrons are negatively charged. A molecule can have: o Two atoms of the same element (oxygen – O2) o Atoms of several different elements (water – H2O) Most of the matter around us has been formed by one or more elements combining in such a way to form completely new substances called compounds. This is called chemical bonding and generally, when atoms bond together, they share or transfer electrons and form molecules. Water is a compound because it is made up of hydrogen and oxygen atoms (H2O). The same is true of carbon dioxide (CO2) and common salt, sodium chloride (NaCl). A compound is matter in which all the molecules are identical, but the molecules are comprised of different atoms in exact proportions. The two or more individual elements are chemically combined to form a separate substance whose characteristics may be completely different from the original element characteristics. All atoms and molecules in matter are constantly in vibratory motion. The degree of motion determines whether it exists as a solid liquid or gas, i.e. its physical state. What we call ‘temperature’ is a measure of this molecular activity. So, at the everyday scale of things, these elements, compounds and mixtures exist as solids, liquids or gases, depending on their internal energy or heat content. The physical state of a compound has no effect on a compound’s chemical structure. Ice, liquid water, and steam are all H2O. A solid has a definite volume and shape and is independent of its container. In a solid there is the least heat energy, and the molecules or atoms do not move very far from their relative position. When heat energy is added to solid matter its molecular vibration increases. This causes the molecules to overcome their rigid shape, and the material changes state from a solid to a liquid. The material’s volume does not significantly change. However, the material conforms to the shape of the container it’s held in. Liquids have definite volume but not shape. As heat energy is continually added to a material, the molecular movement increases further until the liquid reaches a point where individual molecules become independent of each other. The water has changed state again, is now gaseous and called steam. Gases differ from solids and liquids in the fact that they have neither a definite shape nor volume. Chemically, the molecules in a gas are exactly the same as they were in their solid or liquid state. Removing heat will change state back the other way. Steam condenses on a suitable surface and becomes liquid, e.g. clouds, and liquid water freezes solid. 1  It is possible to change the state of most substances by changing their molecular activity. For example, liquid mercury can freeze, solid lead can melt, gaseous oxygen can liquefy. If an element normally exists as a solid (e.g. most metals at room temperature), the easiest way to change its state is to increase or decrease its temperature. As the temperature of the substance is raised, the molecules or atoms gain energy and start to move more freely. This allows the solid to expand initially. As more heat is applied, the molecules or atoms move so freely that they break the bonds of their solidity, but still retain attraction to each other. The substance has melted and the state it has reached is a liquid. If more heat is applied to a liquid, the molecules or atoms gain so much energy that they are capable of breaking their attractive bonds to each other and can break free of the liquid mass. This is vaporization and the liquid is now in a gaseous state. The process is also called ‘boiling’. The reverse, where the gas converts to liquid, is called 'condensation'. At standard sea level pressure of 1013 millibars, water boils at 100°C. At an altitude of 18000 feet where the atmospheric pressure is about 500 millibars, water boils at about 80°C. Increasing or decreasing the pressure on a substance can also change its state. Sometimes solids can become gases without ever becoming liquids. This is called sublimation - e.g. dry Ice” PART 2 (MECHANICS) STATICS A force can be described as that which can produce a change in a body’s state of motion. An application of force will: o Start o Stop o Accelerate, or o Decelerate, a mass If energy is available, then forces can be used to do work. Force is an example of a vector quantity that needs magnitude (size) and direction to be fully defined. Most quantities are scalars and are defined with size only, for example, temperature, length, and time. Either side of the lever below has a moment which is the force multiplied by the distance, from the fulcrum, or pivot (called the arm). 2  The system is balanced when the load moment and the effort moment are equal. A couple is a type of moment which is derived from two equal forces acting in parallel but opposite directions on two different points of a body. The Centre of Gravity (‘CG’ or ‘C of G’) of a body is the point from where the weight appears to act, irrespective of the body’s position. Stress is the force acting through a section of solid material and defined as force per unit area. Strain is the deformation of the material as a result of the stress. If the strain is less than the material’s elastic limit, the elasticity of the material will allow it to return to its natural length. Strain below the elastic limit is directly proportional to the applied stress (Hooke’s Law). Doubling stress will double the strain, (below the elastic limit). If the metal bar was 0.5 m long and extends (deforms) by 2 mm, what is the strain? Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. It is said to be more elastic if it restores itself more precisely to its original configuration – a piano wire is MORE elastic than a rubber band. Tension describes forces that tend to pull an object apart. Flexible steel cable used in aircraft control systems is an example of a component designed to withstand tension loads. Compression is the resistance to an external force that tries to push an object together. The weight of an aircraft causes compressive stress to the runway. Aircraft riveting is performed using compressive forces. When compression loads are applied to the rivet head, the rivet shank will expand until it fills the hole and forms a butt to hold the materials together. Shear stresses occur when external forces distort a body so that adjacent layers of material tend to slide over one another. Shear stress tries to tear a body apart. Shear stress may also occur in fluids, for example a layer of oil or grease between two sliding metal surfaces. Some molecules of lubricant 3 cling to each sliding surface. The subsequent layers of lubricant tend to slide over each other to reduce friction between the metal surfaces. Torsion or torque is a form of shear stress. If a twisting force is applied to a rod that is fixed at one end, the twist will try and slide sections of material over each other. The result is that, in the direction of the twist, there is compression stress and, in the direction, opposite to the twist, tension stress develops. A crack can originate at the point of highest tensile stress in a part. Properties of Solids o The atoms within solids tend to combine in such a manner that the interatomic binding forces are balanced by the very short-range repulsion forces. o Solids cannot flow freely like gases or liquids because the particles are strongly held in fixed positions. o Solids have a fixed surface and volume (at a particular temperature) because of the strong particle attraction. o Solids will expand a little on heating but nothing like as much as liquids because of the greater particle attraction restricting the expansion (contract on cooling). The expansion is caused by the increased strength of particle vibration. o The greatest forces of attraction are between the particles in a solid and they pack together in a neat and ordered arrangement. Properties of Liquids o The primary difference between liquids and solids may be attributed to differences in structure, rather than distance between the atoms. It is these differences in forces between the molecules which give the liquid its flow characteristics while at the same time holding it sufficiently together, to exhibit shape, within a containing vessel. Properties of Gases o Gases flow freely because there are no effective forces of attraction between the particles. o Gases have no surface, and no fixed shape or volume, and because of lack of particle attraction, they spread out and fill any container. o Gases are readily compressed because of the ‘empty’ space between the particles. o The natural rapid and random movement of the particles means that gases readily ‘spread’ or diffuse. Diffusion is fastest in gases where there is more space for them to move and the rate of diffusion increases with increase in temperature. Both liquids and gases are fluids, therefore the theory behind buoyancy and pressure in liquids, such as water, and gases, such as air, is similar. An important difference to remember, though, is that liquids are considered incompressible, that is, have a constant density, while gases are compressible. Pressure is defined as ‘force per unit area’. Barometer is used to measure atmospheric air pressure. KINETICS For linear motion, distance and displacement will be the same Motion is said to be uniform if equal displacements occur in equal periods of time. In other words, constant velocity. Displacement refers to the position of an object relative to its point of origin. This is different to distance which is the total length travelled by an object from its point of origin. A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force 4  A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free-fall. There are two important motion characteristics that are true of free-falling objects: o Free-falling objects do not encounter air resistance o All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 meters per second per second (often approximated as 10 m/s2 for rough calculations) The force that tries to make the ball fly off is Centrifugal Force. In accordance with Newton’s First Law, the object would shoot off on a straight path unless an opposing force is continually applied to keep it turning along the curve. This is termed Centripetal Force. Newtons 3rd Law demands that there is a reaction to this force keeping the string in tension, the Centrifugal Force. The object is accelerated towards the center of the orbit. An object travelling along a curved path tends, at all instants, to fly off on the straight line that forms a tangent to the curve of its path (if the string breaks, for example). Periodic motion or simple harmonic motion (SHM) refers to repeated motion, i.e. that which repeats over time; for example, the mass on a spring (below) or a pendulum. The simple pendulum consists of a weight hanging from a point by a string. If the weight is set swinging, the oscillations are termed periodic motion, and the oscillations are predictable. A system involving the swinging of a mass about a fixed point is described as a pendulum and adheres to strict laws of kinetics. The restoring force acting upon the mass is that of gravity and is proportional to the amplitude of oscillation. Vibration is a term normally reserved for high frequency periodic motion. In an aircraft, rotating or reciprocal components such as engines and propellers produce vibration which can be annoying and destructive. Vibration experienced in an aircraft may originate from the engines, turbulence, or from flight control flutter due to worn hinges or linkage bearings. Constant vibration is annoying to flight crew and passengers. Also, the structure of the aircraft and other components can vibrate in sympathy and structural damage and component wear can occur. Metal fatigue is an example of such structural damage. One example of vibration involves the oscillation of a mass on a spring that is fixed at one end. Harmonics exist as multiples of an original, natural frequency. That is: o The natural frequency is the 1st harmonic, e.g. 100 Hz o The 2nd is at 200 Hz o And the 3rd is at 300 Hz etc. Harmonics can cause resonance as well as natural frequencies. The natural or resonant frequency of an object is the frequency where that object vibrates naturally, or without an external force. If two objects have the same natural frequency and are joined to each other, when one of them vibrates, it can transfer its wave energy to the other object making it vibrate. This transfer of energy is known as resonance Velocity Ratio is the direct ratio of two speeds that may be present in the same system. For example, consider a pulley system that uses a Mechanical Advantage of 4. The operator will pull through a one meter of rope to raise the load by 0.25m. Therefore, the rope moves 4 times as fast as the load is being raised. The velocity ratio is 4:1. Mechanical Advantage (MA) = Velocity Ratio (VR) 5  A lever is an example of a simple machine, which is a device used to gain a Mechanical Advantage (MA). In other words, the multiplication of a force by the use of leverage. The mechanical advantage of a first-class lever depends on the distance moved by effort compared to load and is equal to: The efficiency of a machine compares the output work to the input work. Efficiency of a machine is expressed as a percentage. The higher the percentage, the more efficient the machine. No machine is 100% efficient due to friction and other losses. DYNAMICS Dynamics is the study of forces at work in motion, and the use of energy. The Earth is a large mass in space and there is a mutual attraction between it and everything on its surface. Because the Earth is so much bigger than everything else, it seems like the attraction is only one way. Newton's Laws of Motion provide the reasoning that force equals mass multiplied by acceleration, F = ma Mass is the amount of matter contained in a body. This value does not vary. Weight varies according to the gravitational field acting on that body. A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction. For simplicity’s sake, all forces (interactions) between objects can be placed into two broad categories: o contact forces, and o forces resulting from action-at-a-distance Contact forces are those types of forces that result when the two interacting objects are perceived to be physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. Action-at-a-distance forces are those types of forces that result even when the two interacting objects are not in physical contact with each other; yet are able to exert a push or pull despite their physical separation. Examples of action-at-a-distance forces include gravitational forces. Newton’s Second Law of motion states o “The acceleration of a body is directly proportional to the force applied to it and is inversely proportional to the mass of the body”. o F = ma (force equals mass multiplied by acceleration). When a force acts on an object, giving it motion, it gains momentum. Once an object has momentum, it takes more force to change the motion. Inertia is the property of a mass which causes it to resist any change in its state of motion. Newton’s first law of motion states: o “A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force.” The larger the mass: the greater the inertia. When a force acts on an object, overcomes inertia, and sets it in motion, work is done. Unless the object moves through a distance the work done is said to be zero. Work done is found by the formula: W = Fs 6  o Where F = force, s = distance The unit of work in the SI system is the joule, which equals 1 Newton meter (Nm) If an object is moved 10 meters by a force of 100 newtons, the work is calculated as 1000 joules In the Imperial system of measurement, a measure of work is the foot-pound, the effort of raising one pound of mass by one foot. Power is the rate of doing work. When determining the amount of work done, the time required to do the work is not considered. Power on the other hand takes time into consideration. For example, if a person climbs a flight of stairs, they perform the same amount of work whether they walk up or run up. However, when the person runs up they are working at a faster rate and therefore using more power. P=W/ t The unit SI unit of power is the watt. One watt is the power generated when one joule of work is done in one second. In the imperial system of measurement, power is expressed in foot/pounds per second and one horsepower is equivalent to 550 foot/pounds per second and 746 Watts. Energy provides the capacity for work to be done and effect change. The SI unit of energy is the joule. One joule of energy can do one joule of work assuming there have been no losses like friction. An important concept when thinking about energy is the law of the conservation of energy which states: o Energy can neither be created nor destroyed. It can only be changed from one form to another. For example, a car turns the chemical energy found in petrol into mechanical energy, heat and sound. The potential energy in a body or of a body means stored energy, stored in the body because of its position, condition or chemical nature. Even though an object is not doing work, it can still be capable of doing work. For example, a mass held above the ground. While it is being held it has no motion, so it is not doing work. If it is then released, it will fall immediately, thus doing work. Kinetic energy is energy a body has because of its motion. If a body is held aloft and then released, as it starts to fall to ground the potential energy is converted to kinetic energy. In accordance with the law of conservation of energy, the total energy does not change, but potential energy can be transformed into kinetic energy and vice-versa. Heat is one of the most useful forms of energy because of its direct relationship with work, and with the use of engines. Other types of energy can be transformed, in accordance with the law of conservation of energy, into heat. Heat is also found as a consequence of friction. The heat produced by friction is usually unwanted. With any machinery, the efficiency is the ratio of work output to work or energy input. If 100 joules of work is put into a gear train and the output is 90 joules, the efficiency is said to be 90% It is friction that primarily determines the efficiency of a machine, because the friction between moving parts creates heat, sound and sometimes light. All of these are classified as energy losses. Reducing friction is usually accomplished by lubrication or streamlining. Inertia has been defined as the tendency of a mass to resist changes in its state of motion. Momentum, however, is the product of this inertia and the motion it already has. There are two types of momentum, linear and angular. 7  Linear momentum is a measure of the tendency of a moving body to continue in motion along a straight line. Momentum is defined as the product of the mass and velocity of a body. M = mv Angular momentum is a measure of the tendency of a rotating body to continue to spin about an axis. o M = mω where ω is the rpm or angular velocity. If a force is applied to a moving body, that body’s state of motion is altered. The momentum of the body is changed by an amount called the Impulse. (Impulse) I = Ft (Force multiplied by time) A spacecraft’s “burn” i.e. applying thrust for a number of seconds is an example of an Impulse. Likewise, an aircraft thrust input is a force which changes the motion of the aircraft. Applying force for a period of time will create an impulse. A gyroscope is any rotating mass which then possess angular momentum. A useful example is the type consisting of a rotor mounted on gimbals, so that it’s supporting platform or case can be turned in one or more planes around the rotor without changing the rotor’s plane of rotation. Like all rotating masses, the gyroscope has two fundamental characteristics. These are gyroscopic inertia (rigidity in space) and precession. Gyroscopic Inertia (rigidity in space) o This is the natural property of any rotating mass to resist changes to its plane of rotation, unless an external force causes a change. This is the reason a spinning top or coin remains upright until it runs down. If the rotor is in a case securely fitted to the airframe, it will show changes of aircraft attitude. o This is the basis for the instrument called the Artificial Horizon or Attitude Indicator. Precession o This is the change of the plane of rotation caused by an external force. o If a force is applied to the rotating mass, overcoming the natural rigidity, then its plane of rotation will deflect 90° in the direction of rotation. When objects move they usually roll or slide in contact with other objects or substances. Such sliding or rolling contacts have resistance to the force that causes the motion. This resistance is called friction. There are four types of friction: o Starting (static) - Overcoming initial resistance until breakaway occurs. o Sliding - Resistance during steady motion. o Rolling (kinetic) - Single point contact resistance is less than sliding. o Fluid friction - occurs when an object moves through a fluid, meaning either a liquid or a gas The coefficient of friction refers to the differences in friction between various materials. The higher the coefficient of friction (μ – the Greek letter ‘mu’), the greater the resistance between the two surfaces. The amount of sliding friction can be calculated from the relationship: o F=μN o Where N is the reaction to the weight of the object from the surface on which it is sliding, and F is the quantity of frictional resistance. Coefficients of rolling resistance are very small Rolling one surface over another creates less friction than sliding one surface over another. FLUID DYNAMICS 8  Specific gravity is calculated by comparing the weight of a definite volume of substance with the weight of an equal volume of water Specific gravity is not expressed in units, but as a pure number A device called a hydrometer is used to measure the specific gravity of liquids. Gasoline has a specific gravity of 0.72, which means its weight is 72% of the same amount of water. The SG of aviation fuel varies due to a variety of factors such as: o Refining process o Storage facilities o Ambient conditions The SG of a fuel supply must be confirmed in order to calculate how many liters will provide the weight of fuel required for a flight. The density of a substance is its weight per unit volume. (Note: It should be “mass per unit volume”; “weight per unit volume” is written in the book) The density of solids and liquids varies with temperature. However, the density of a gas varies with temperature and pressure. Because the density of solids and liquids vary with temperature, a standard temperature of 4°C is used when measuring the density of each. Both liquids and gases can flow, and are called fluids. Some fluids flow more readily than others. The term viscosity is defined as the resistance of a fluid to flow. Viscosity is one of the most important properties of hydraulic fluids. It is a measure of a fluid’s resistance to flow. A liquid, such as gasoline, which flows easily, has a low viscosity; and a liquid, such as oil, which flows slowly has a high viscosity. Oil is more resistant to flow than water, making oil more viscous. Don’t confuse viscosity with density – water is heavier than oil. Oil will float on water. Water will sink to the bottom of a fuel tank. The viscosity of a liquid is affected by changes in temperature and pressure. As the temperature of a liquid increases, its viscosity decreases. That is, a liquid flows more easily when it is hot than when it is cold. The viscosity of a liquid increases as the pressure on the liquid increases. The term Viscosity is used mostly regarding liquids, especially oils, but it also applies to gases. The viscosity of air is a consideration in aerodynamics. When the temperature of a gas rises, it becomes more viscous. In other words, the viscosity of gases varies directly with temperature, and the viscosity of liquids varies inversely with temperature. That is, when the temperature of a gas rises, it becomes more viscous. The viscosity index (V.I.) of oil is a number that indicates the effect of temperature changes on the viscosity of the oil. Viscosity is the resistance of a fluid to flow. So, a fluid can flow at different rates if its viscosity changes with temperature. Viscous liquids are often used for lubrication because they resist flowing away from their prime purpose, which is to stick between surfaces to reduce friction. Therefore, in most applications, resistance to flow is a positive property. A flat shape fights air flow and causes more drag or resistance. A curved shape allows air to flow smoothly around it. This is attached flow (Coanda effect). 9  Streamlining is the smooth shaping of an object, such as an aircraft body or wing, to reduce the amount of drag or resistance air, due to viscosity, to motion through a stream of air (moving through viscous air). Streamlining makes the flight more efficient. The reduction in turbulent air allows this efficiency. Streamlining reduces the amount of resistance and increases lift. Generally, for theoretical and experimental purposes, gases are assumed to be incompressible when they are moving at low speeds--under approximately 220 miles per hour. However, when aircraft began travelling faster than 220 miles per hour, assumptions regarding the air through which they flew that were true at slower speeds were no longer valid. At high speeds some of the energy of the quickly moving aircraft goes into compressing the fluid (the air) and changing its density. The air at higher altitudes where these aircraft fly also has lower density than air nearer to the Earth's surface. The airflow is now compressible, and aerodynamic theories have had to reflect this At lower altitudes, air has a higher density and is considered incompressible for theoretical and experimental purposes. Air at sea level has a certain atmospheric pressure. This pressure is due to the weight of the atmosphere above it. Although the air pressure changes with changing weather, this relatively constant pressure is called static pressure. If an aircraft is not moving, its instruments will sense this static pressure A moving aircraft also has forward, dynamic, motion which means that it is striking air molecules at a rate proportional to its Kinetic Energy. (speed squared), (Dynamic pressure). Dynamic Pressure is known as 'q' and = ½ρV2 where ρ is the fluid density and V is the fluid velocity. The sum of the static and dynamic pressure is the total pressure (Pt or P0), also known as the pitot pressure, or stagnation pressure of the fluid. In an aircraft, Static Pressure is measured perpendicular to the airflow through a hole. Total Pressure is captured by an open tube parallel to the airflow (Pitot tube). Dynamic Pressure is then obtained as Total P – Static P and provided to the pilot as the Indicated Airspeed (IAS) – a measure of the aerodynamic force available at that speed and altitude. 10  Static pressure is the actual pressure of the fluid, which is associated not with its motion but with its state. In aircraft, static pressure is open to the atmosphere and is measured perpendicular to the airflow through a hole in the wall. Bernoulli's Theorem Equation o Static Pressure + Dynamic Pressure = Total Pressure = Constant An extension of Bernoulli’s Theorem is the basis of how some of the lift is generated by aircraft wings, propellers and helicopter rotor blades. The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. An equation for the drop in pressure due to the Venturi effect may be derived from a combination of Bernoulli's principle and the equation of continuity. PART 3 (THERMODYNAMICS) Temperature represents the degree of heat possessed by one mass over another. When heat flows from one body to another, the hotter is said to be at a higher temperature. Temperature represents the average kinetic energy of atoms and molecules and is measured in degrees (°). As the temperature increases, the molecular activity increases, and vice versa. All molecular activity ceases at a point known as 'absolute zero'. When the thermal changes have stopped, we say that the two objects (or systems) are in thermal equilibrium. We can then define the temperature of the system by saying that the temperature is that quantity which is the same for both systems when they are in thermal equilibrium. One of the 'systems' mentioned above could be an instrument calibrated to measure temperature - i.e. a thermometer. A thermometer is an instrument that measures the temperature of a system in a quantitative way. The easiest way to do this is to find a substance having a property that changes in a regular way with its temperature. The most direct 'regular' way is a linear one: o t(x) = ax + b For example, the element mercury is liquid in the temperature range of -38.9° C to 356.7° C. As a liquid, mercury expands as it gets warmer; its expansion rate is linear and can be accurately calibrated. There are four main temperature scales: o degrees Celsius (°C) o degrees Fahrenheit (°F) o degrees Rankine (°R) o Kelvin (K) Celsius o This provides fixed marks to calibrate the tube, for example, calling the melting point of pure ice 0° and the boiling point of pure water 100° gives us the centigrade or Celsius scale divided into 100-degree increments. Kelvin o The Kelvin scale also has 100 increments between the freezing and boiling point of water, but zero on the Kelvin scale represents the minimum temperature at which all molecular activity ceases (absolute zero). This point is equivalent to – 273°C. o With the Kelvin scale, the unit ‘degrees’ and its symbol (°) is not used. It is said that water boils at 373 K. 11  Fahrenheit o The Fahrenheit scale has 180-degree increments between the freezing point and boiling point of water. The freezing point is at 32°F and the boiling point is 212°F. o There are 5 Celsius degrees to every 9 Fahrenheit degrees. Heat is one form of energy, and in many cases the production of heat and its subsequent release can do useful work. Heat is a kinetic energy associated with the motion of atoms or molecules and capable of being transmitted through solid by conduction and through fluid media by convection, and through empty space by radiation. Units of Heat o Calorie (cal): one calorie is the quantity of heat required to raise the temperature of one gram of water by one degree Celsius. o British Thermal Unit (BTU): one BTU is the quantity of heat required to raise the temperature of one pound of water by one degree Fahrenheit. o Joule (J): the SI unit for all forms of energy. Energy provides the capacity for work to be done. One joule of energy can do one joule of work. There are 4.2 J per calorie. Temperature represents the degree of heat possessed by one mass over another. When heat flows from one body to another, the hotter is said to be at a higher temperature. However, a cup of water at 90°C contains less heat than a swimming pool at 20°C. For this reason, we define two properties, one called the Specific Heat of a substance, and the other, the Heat Capacity. The heat capacity (C) of a substance is the amount of heat required to change its temperature by one degree and has units of energy per degree. The specific heat of a substance is the number of calories required to raise the temperature of 1 gram of the substance by 1°C or the number of BTUs required to raise the temperature of 1 pound of the substance by 1°F. Water is used as the benchmark as it takes 1 calorie to raise 1 gram of water by 1°C. Other substances, notably metals, take very much less energy to raise their temperature. The high specific heat of water is why ocean temperature does not vary as much as land temperature. This allows the oceans and large lakes of the earth to act as heat sinks or temperature stabilizers. Conduction requires physical contact between a body having a high level of heat energy and a body having a lower level of heat energy. An example of heat transfer by conduction is the removal of heat from an engine cylinder by cooling fins. Convection is the process by which heat is transferred by bulk movement of a fluid. As fluid is heated by a heat source, it becomes less dense and rises, being replaced by cooler fluid. Heating water in a kettle, heating air in a house and the circulation of atmospheric heat are examples of convection. Electromagnetic Radiation refers to the emission of energy from the surface of most objects and is related to the acceleration of charged particles. Radiation is the process by which heat is transferred by movement through a gas. Conduction and convection take place relatively slowly while radiation takes place at the speed of light (Note: Radiation takes place at the speed of light in vacuum. All forms of matter emit radiation. In solids, liquids, and gases it can either be treated either as a surface or a volumetric phenomenon). 12  The temperature of a body is a measure of the average kinetic energy of the molecules of that body. It follows that molecules of warm liquids and gases move around faster in their containers than molecules of cool liquids and gases. As a solid is heated its molecules vibrate faster about their equilibrium positions. As a result of this increased motion of molecules as they are heated, solids and liquids expand as the temperature is raised. First law of thermodynamics is like the law of conservation of energy: o “Heat energy cannot be destroyed; it can only be changed from one form of energy to another”. o For example, the heat energy of combustion in an engine is transformed into mechanical energy, but there are losses or inefficiencies as some of the energy is transformed to sound energy. Second law of thermodynamics states that: o “Heat cannot flow from a body of a given temperature to a body of a higher temperature”. o That is, heat will only flow from a warmer body to a cooler body. o This is a logical process and the theory behind it is used in car radiators, heat exchangers, oil coolers etc. It has been stated that gases differ from solids and liquids by being compressible. This affects how they transmit forces that can use the thermal energy to effect change by doing useful work. Gas Laws o Boyle’s Law ▪ The volume of a confined body of gas varies inversely as pressure varies, assuming temperature remains constant. ▪ This is called an Isothermal process o Charle’s Law ▪ The volume of a gas varies in direct proportion to its temperature, assuming pressure remains constant o Gay-Lussac’s Law ▪ This third gas law relates the absolute pressure to the absolute temperature of a gas when its volume is held constant. For solids and liquids, in S.I. we can simply define the specific heat capacity (s.h.c.) as the quantity of energy, measured in kilojoules (kJ), that will raise the temperature of one kilogram (kg) of the body by 1 Kelvin (K). For gases, however, there must be an additional qualifier. It is necessary to state the conditions under which the change of temperature takes place, since a change of temperature can produce large changes of pressure or volume depending on whether or not the gas is confined inside a closed container. Gases have two values specific heat capacity: o The specific heat capacity at constant volume (Cv) is defined as the quantity of heat required to raise the temperature of 1 kg of the gas by 1 K when the gas is heated while enclosed within a constant volume. An example of a constant volume process is the pressure rise inside an aerosol can after it has been put on a fire and before it bursts. o The specific heat capacity at constant pressure (Cp) is defined as the quantity of heat required to raise the temperature of 1 kg of the gas by 1 K if the pressure of the gas remains constant. This can only be possible if the gas is free to expand. An example of a constant pressure process is the heating of air to fill a hot air balloon. Heat energy is added to the air, which expands to fill the balloon at atmospheric pressure. 13  The s.h.c. at constant pressure (Cp) is always greater than the s.h.c. at constant volume (cv), since if the volume of the gas increases, work must be done by the gas to push back the surroundings. Sometimes heat is not an unwanted by-product of combustion. Sometimes the expansion of gas created by the heat is the prime purpose for the combustion. For example, when a gun fires a bullet, the heat produced by the ignition of a small pyrotechnic charge increases the volume of gas available to push the bullet out of the barrel. Heat is necessary for the process to occur. Likewise, a gas turbine engine relies on heat to expand gas. The expanded volume of gas drives the engine turbines and contributes to the reactive force of thrust. In this sense, expanding gases do work similar to other mechanical processes. Remember, work is calculated by multiplying the force applied by distance: o W = Fs The greater the force applied to an object or the greater the distance an object moves, the more work has been done. If expanding gases in a rifle create a force of 10,000 newtons and move bullet 0.5 meters along the barrel of the rifle: o W=F x s o W= 10,000 x 0.5 o W=5,000 Joules of Work has been expended Remember, also, that power is the time rate of doing work. A man may expend 5,000 joules pushing a wheelbarrow for 1 hour. The rifle has expended the 5,000 joules in a split second. It has generated a great deal more power than the wheelbarrow man. Isothermal means constant temperature Isothermal change is a change in the volume and pressure of a substance, which takes place at constant temperature. For gases, Boyle’s Law is isothermal. The vaporization and condensation of refrigerant in the heat exchangers of a vapor cycle air conditioning system is isothermal. Welding gas bottles left out in the sun could over pressurize, hence the need for relief valves. BBQ gas suddenly released to a lower pressure feels very cold on your fingers. The temperature change could occur without the addition of external heat or removal of heat by external means. A temperature change like this is called an adiabatic process. Another example is the increase in cylinder temperature when the fill rate is too high. An adiabatic process occurs without interchange of heat energy with the surroundings, i.e. heat energy does not flow into or out of the process. Note that the definition refers to heat energy, not temperature. Large changes of temperature can occur in an adiabatic process. An example of a (nearly) adiabatic process is the compression of air in a piston engine or gas turbine engine. Air, initially at atmospheric pressure, is reduced in volume by mechanical means. As the volume decreases, both the temperature and pressure rise dramatically. Temperature rises because of the reduction of volume, not because of heat energy flowing inwards. The process is nearly perfectly adiabatic because it happens so fast that there is no time for significant heat energy to exit the process by contact with the walls of the compressor. Yes, the compressor gets hot, but this represents a small fraction of the total energy in the process. An example of an adiabatic process in the opposite sense is the rate of decrease of temperature, which occurs when a parcel of warm air rises adiabatically through the atmosphere. As the air rises, it 14 encounters lower atmospheric pressure, which allows it to expand, which causes a temperature reduction. No heat energy leaves the process. The temperature reduction is the result of expansion. Engine cycles In both piston engines and gas turbine engines, the compression of air is necessary before fuel is introduced and ignited. In both these types of engines there is a significant increase in temperature of the air medium due to this compression process. Piston Engine (Otto Cycle) o Intake o Compression (15:1) o Combustion (Power) o Exhaust Multiple cylinders connected to the same crankshaft increase the number of power strokes per revolution. Gas Turbine Engine (Brayton Cycle) o Intake o Compression o Combustion o Expansion o Exhaust Turboprop o Extra turbines transfer the power to a propeller. 15  Turbofan o The extra turbines transfer the power to a multi-bladed and shrouded fan which accelerates the air mass similarly to a propeller. About 70% of the thrust is from the fan. Turboshaft o These are similar to turboprops and fan engine in that they utilize extra turbines to deliver the power to a variety of applications, such as electrical generators, ship’s propellers, and helicopter rotors. Refrigerators o The compressed gas heats up as it is pressurized. The coils on the back of the refrigerator let the hot refrigerant gas dissipate its heat. The refrigerant gas condenses into refrigerant liquid (dark blue) at high pressure. o The high-pressure refrigerant liquid flows through the expansion valve. o The liquid refrigerant immediately boils and vaporizes using its own latent heat (light blue), its temperature dropping to -27 F. This makes the inside of the refrigerator cold. The cold refrigerant gas is sucked up by the compressor, and the cycle repeats. 16  Air-Conditioning (Cold Cycle) Air-Conditioning (Reverse Cycle) Heat Pump The amount of heat required to melt a solid is called the latent heat of fusion. The amount of heat extracted to solidify a liquid is still called the latent heat of fusion. The amount of heat required to boil or vaporize the liquid is called the latent heat of vaporization (or evaporation). The amount of heat extracted to condense a vapor is still called the latent heat of vaporization (or evaporation). Energy concerning the application, loss or transfer of heat is termed thermal energy. Any time fuel is burnt (combustion), heat is produced. Sometimes the heat is useful and sometimes the heat is unwanted. We say that heat is a by-product of the combustion process. According to the law of conservation of energy, thermal energy cannot be created or destroyed, but it is converted from, and to, other forms of energy. For example, thermal energy may be created from electrical, chemical, mechanical or nuclear energy. It can be converted to mechanical or kinetic energy. The heat in a thermal process can also add energy to chemical reactions. Thermal energy can be transferred from one object or system to another in the form of heat. In a gas turbine (jet) engine, the heat of combustion is necessary to expand gases and do work while flowing through the engine. 17  PART 4 (OPTICS) Visible light is Electromagnetic Radiation that is detectable by the human eye. The speed of EMR propagation C, commonly called the speed of light is 3 x 108 m/s in a vacuum (300,000 km/s or 186,000 miles per second). Visible light, (often called white light) comprises of all of the EMR between 400 and 700 nm (nanometers), that is, between blue and red in the spectrum. The law of reflection states that the angle of incidence equals the angle of reflection. The angles are measured against a line perpendicular to the surface of the reflective material, called the ‘normal’. Reflection of light and other electromagnetic radiation occurs when waves encounter a boundary that does not absorb the radiation’s energy and bounces the waves off the surface. The incoming wave is known as the incident wave and the wave that is bounced from the surface is called the reflected wave. When light waves pass from one transparent medium to another, they change velocity and direction. The angle of refraction is dependent on the density of the material through which the light passes. For example, when light travels from air to water, it slows down and bends towards the normal. Most substances have a refraction index (n) which gives an indication of their density, how much the light slows down and, therefore, how much the light bends through the substance. The higher the refractive index number, the denser the material and the more the light will slow down and refract or bend as it passes through the substance. 18  Reflection off a plane surface: o Note: direction of energy propagation gets reversed. o If we have an extended object, this will create an image. To find out where the image appears to be, extend the line of sight. o To get the sensation of depth, we need binocular vision Spherical mirrors o Light from the center of a spherical mirror is reflected back o Concave mirror o Convex mirror 19  The use of lenses is an application of refraction. Light is bent as it passes through transparent material of different densities. There are a variety of lenses, but essentially, they are: o Converging or positive (convex) ▪ Real image from a converging lens (Note: Image is inverted and enlarged) o Diverging or negative (concave) ▪ Virtual images are formed by diverging lenses. Image is upright but diminished. The most important quantity for a lens is the focal length (f) i.e. how far from the lens do parallel rays get focused. As the incidence angle (i), increases, less and less energy is refracted, and more is reflected (r). At the Critical Angle, 100% of the light is reflected and Total Internal Reflection is occurring. This phenomenon is important in the design of fiber optic cable. 20  An optical fiber is a thin strand of high-quality glass. Very little light is absorbed in the glass. Light getting in at one end is totally internally reflected, even when the fiber is bent. Fiber optics are also used in medicine in flexible inspection probes which can carry a low heat light source and transmit images back to an eyepiece or video screen. PART 5 (WAVE MOTION & SOUND) When energy is transferred by the passage of a periodic disturbance through an elastic medium, it is said to be in Wave Motion. These waves are called transverse and can be represented by a graph of the values of Sin θ between 0° and 360° (Sinusoidal wave motion). Mechanical waves transfer energy through a medium and can be classified as transverse or longitudinal according to how they travel. o Sound waves have been identified as longitudinal compression waves travelling through an elastic medium, of which air is a good example. o These are called compression or longitudinal waves and are a set of pulses through a medium. However, they can be mapped as sinusoidal waves. o A spring is a longitudinal compression wave. Light waves are different again. They are the type of Electromagnetic Radiation that is detectable by the human eye. EMR is energy propagation by periodic variation of the electric and magnetic field strengths caused by the acceleration of charged particles. They are not mechanical waves, but they display similar behavior, and are able to travel through vacuum. Interference Phenomena (Superposition) o When waves converge, their effect is algebraically added. 21  Standing waves are formed when a wave interferes with its own reflection. This will occur when the medium is secured at both ends like a guitar string or a structural member. Standing waves are formed when a fundamental wave (the longest wavelength that can fit in a tube or on a string) is subjected to interference and a harmonic wave is produced (a multiple of the original, fundamental wave). Sound waves are compression waves because they use the mechanical action of molecules to transfer their action through a medium. For this reason, sound waves cannot travel through a vacuum. The ‘slinky spring’ below demonstrates this action. The coils undergo compression, followed by rarefaction when the coils open out. This is the mechanism of a sound wave through air. 22  Suppose we tune two strings of a guitar to vibrate at almost, but not quite, the same frequency. Plucked simultaneously, the volume of the sound produced by them appears to rise and fall continuously. This rise and fall has a fixed frequency called the beat frequency. Sound waves originate in some vibrating body such as the oscillation of a person's vocal cords or the periodic rotation of a plane’s propeller and travel through the air or some other material medium. As the source of sound vibrates, the air surrounding the source is periodically compressed and rarefied (made less dense). This periodic change in the atmospheric density and therefore pressure, moves forward with a definite speed of propagation called the "speed of sound". Sound waves are usually defined as pressure waves of frequencies which our brains can interpret. The eardrum would be affected by all pressure waves, but only those frequencies, between 20 Hz to 20,000 Hz, are “heard” by most humans. The speed of sound in air is dependent on the temperature of the air. This is not surprising since the molecules of air move faster in their random motion if the temperature is higher. Thus, we should expect these pressure waves to move somewhat more rapidly in warmer air. Sound travels faster in liquids, and even faster still, in solids. Sound waves have been identified as longitudinal compression waves travelling through an elastic medium, of which air is a good example. These waves propagate at a speed which varies according to the medium through which it travels. Speed of sound in air varies according to atmospheric temperature. In normal atmospheric conditions at sea level, it is 660 kt (knots) which equates to about 340 m/s, or 1,224 km/h. An aircraft creates disturbances to the air as it moves through it. These disturbances act like sound waves and travel at the same speed but are of insufficient intensity to be detected by the human ear. Less than speed of sound (Subsonic) More than speed of sound (Supersonic) The speed of sound in a medium varies with the properties of elasticity and temperature. Intensity is determined by the amplitude of the sound wave and is measured in Watts per 2 metre ; however, it is more convenient to express a sound as a relative quantity called Intensity Level. The Intensity Level (IL) of sound waves is measured in a unit called the decibel (dB) It should be noted that 120dB is the “threshold of pain". Sound of this intensity is painful to the normal ear. If the ear is continuously subjected to sound of this intensity, ear damage and hearing loss can result. 23  The intensity of sound decreases (inversely) with the square of the distance from the source of sound. Therefore, doubling the distance from a source of sound decreases the intensity to one-fourth of the previous value. The frequency of the sound determines its pitch. The faster the air vibrates, the higher the pitch, and the faster the wavelengths pass the listener. Quality or “timbre” of sound depends on the nature of the harmonics present. You will recall that harmonics are numerical multiples of the original frequency. Doppler effect o When a source of sound is not moving, the sound waves radiate out from the source like ripples in a pond (A above). o When the source of sound moves, however, the frequency (and pitch) ahead of the source becomes higher than the frequency behind it (B above). o This change in frequency is called the Doppler Effect. It accounts for the sound of sirens, motorbikes, and aircraft etc. becoming higher pitched as they approach, then decreasing in pitch as the vehicle passes. o Any energy propagated by means of wave motion is subject to the Doppler Effect. o Examples include light, which helped astronomers develop the Big Bang model, and radio waves, which provide navigational information. 24