Physics 1 PDF - Fluid Mechanics, Thermodynamics

Physics 1 Fluid mechanics. Thermodynamical parameters. Temperature and heat. Assoc. prof. dr. Kristina Bočkutė  Minutes from the last lecture o A mechanical wave travels within some material called the medium. The wave function is used to describe the displacement of particles in the medium....

Physics 1 Fluid mechanics. Thermodynamical parameters. Temperature and heat. Assoc. prof. dr. Kristina Bočkutė  Minutes from the last lecture o A mechanical wave travels within some material called the medium. The wave function is used to describe the displacement of particles in the medium. o Waves can be transverse and longitudinal. Surface waves. o Principle of superposition. o Sound consists of longitudinal waves in a medium. o Standing waves. o Doppler effect. 2  Minutes from the last lecture A sinusoidal transverse wave is traveling on a string. Any point on the string: A) Moves in the same direction as the wave B) Moves in simple harmonic motion with a different frequency than that of the wave C) Moves in simple harmonic motion with the same angular frequency as the wave D) Moves in uniform circular motion with the same angular frequency as the wave 3  Minutes from the last lecture Any point on a string carrying a sinusoidal wave is moving with its maximum speed when: A) The magnitude of its acceleration is a maximum B) The magnitude of its displacement is a maximum C) The magnitude of its displacement is a minimum D) The magnitude of its displacement is half the amplitude E) The magnitude of its displacement is 1/4 the amplitude 4  Minutes from the last lecture A standing wave: A) Can be constructed from two very similar waves traveling in opposite directions B) Must be transverse C) Must be longitudinal D) Has motionless points that are closer than half a wavelength E) Has a wave velocity that differs by a factor of two from what it would be for a traveling wave 5  FLUID MECHANICS. THERMODYNAMICS o Fluid mechanics Fluids; Quantities describing fluids (density, volume, pressure); Fluid dynamics. o Thermodynamics Macroscopic description of matter; Temperature; Heat. o Summary; o Next lecture. 6 Introduction States of matter o Solid o Liquid o Gas / Vapor o Plasma o A fluid is a substance that flows. Both gases and liquids are fluids. o Because they flow, fluids take the shape of their container rather than retaining a shape of their own. o The detailed behaviour of gases and especially liquids can be complex. o Behaviour is described using methods (macroscopic and microscopic). 7  Molecular Model of Gases and Liquids Gases and liquids are fluids – they flow and exert pressure. o Gases Molecules move freely through space. Molecules do not interact except for occasional collisions with each other or the walls. Molecules are far apart, so a gas is compressible. o Liquids Molecules are weakly bound and stay close together. A liquid is incompressible because the molecules can’t get any closer. Weak bonds allow the molecules to move around. 8 Molecular Model of Gases and Liquids Attractive forces tend to bind atoms and molecules together Kinetic energy counteracts this tendency. 9 Molecular Model of Gases and Liquids If the total kinetic energy of atoms and molecules is much higher than the total potential energy of their attraction, then the substance is in a gaseous state. If the kinetic energy of molecules (its modulus) is much lower - solids. 10 The liquid state is formed when these energies are close. Liquids In liquid molecules interact strongly by maintaining mutual bonds, but move much more freely than molecules in a solid state. The liquid state is distinguished by the fact that the material tries to maintain its volume, but does not retain its shape. 11 Liquids Liquid molecule in 1 s can to change its position about 108 times, making 108 - 105 vibrations between two jumps. 12 Liquids Fluids in critical condition does not have serious friction. Even the slightest force causes fluid particles to move. Internal friction (viscosity) is noticeable in real liquids - it is a certain resistance. 13  Liquids Shape of the liquid depends on the shape of the container. Real liquids are characterized by compressibility, ie. when liquids are compressed, their volume decreases slightly. All phenomena related to viscosity and density make it difficult to study the movement of liquids. 14  Liquids Theoretical models deal with the motion of inviscid and incompressible fluids, called ideal fluids, for which the following laws apply: a. Pascal, b. Law of Communicating Vessels, c. Archimedes. 15 Volume and Density One important parameter that characterizes a macroscopic system is its volume V, the amount of space the system occupies. The SI unit of volume is m3. Volume conversion: 1 m3 = 106 cm3 1L = 1000 cm3, so 1 m3 = 103 L. 1 mL = 1 cm3. A system is also characterized by its mass density – the ratio of mass m to volume V: 𝑚 𝜌= 𝑉 The SI units of mass density is kg/m3. Quite often g/cm3 are used. 1g/cm3 = 1000 kg/m3. 16  Volume and Density The mass density is independent of the object’s size. Mass and volume are parameters that characterize a specific piece of some substance – say copper – whereas the mass density characterizes the substance itself. The density of a material depends on environmental factors such as temperature and pressure 17  Pressure A fluid exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid. We define the pressure p at the point of fluid as the normal force per unit area: 𝑑𝐹⊥ 𝐹⊥ 𝑝= or 𝑝= 𝑑𝐴 𝐴 Force due to The pressure is pressure the same at all 𝐹 = 𝑝𝐴 points. Pressure is a scalar. The SI unit of pressure is the pascal, where 1 pascal = 1 Pa = 1 N/m2. 18 1 bar = 105 Pa; 1 mbar = 100 Pa.  Pressure Atmospheric pressure pa is the pressure of the earth’s atmosphere, the average air pressure at sea level at a temperature of 15 degrees Celsius. This pressure varies with weather changes and with elevation. The global average sea-level pressure is 101 325 Pa. Consequently, we define the standard atmosphere as 1 standard atmosphere = 1 atm ≡ 101 325 Pa = 101.3 kPa 1 atm = 1.013 bar 19 Pressure in Liquids Gravity causes a liquid to fill the bottom of a container. Thus the pressure in a liquid is due almost entirely to the gravitational contribution (weight is not negligible). The volume of fluid element is 𝑑𝑉 = 𝐴𝑑𝑦, its mass is 𝑑𝑚 = 𝜌𝑑𝑉, and its weight 𝑑𝑤 = 𝑑𝑚𝑔 = 𝜌𝑔𝐴𝑑𝑦. If the pressure at the bottom surface is p, then the pressure at the top surface is 𝑝 + 𝑑𝑝. The fluid element is in equilibrium, so the total y-component of force, including the weight and the forces at the bottom and top surfaces, must be zero: Σ 𝐹𝑦 = 0 𝑝𝐴 − 𝑝 + 𝑑𝑝 𝐴 − 𝜌𝑔𝐴𝑑𝑦 = 0 20 Pressure in Liquids 𝑑𝑝 𝑝𝐴 − 𝑝 + 𝑑𝑝 𝐴 − 𝜌𝑔𝐴𝑑𝑦 = 0 = −𝜌𝑔 𝑑𝑦 When y increases, p decreases; that is, as we move upward the fluid, pressure decreases. If 𝑝1 and 𝑝2 are the pressures at elevations 𝑦1 and 𝑦2 , respectively, and if 𝜌 and 𝑔 are constant, then 𝑝2 − 𝑝1 = −𝜌𝑔(𝑦2 − 𝑦1) Pressure in a fluid of uniform density in respect of the pressure at the surface (𝑝0): 𝑝 = 𝑝0 + 𝜌𝑔ℎ The pressure at a depth ℎ = 𝑦2 − 𝑦1 is greater than the pressure 𝑝0 at the surface by an amount 𝜌𝑔ℎ. 21  Pressure in Liquids 𝑝 = 𝑝0 + 𝜌𝑔ℎ If we increase the pressure 𝑝0 at the top surface, the pressure 𝑝 at any depth increases by exactly the same amount. Pascal’s law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. 𝐹1 𝐹2 𝑝= = 𝐴1 𝐴2 𝐴2 𝐹2 = 𝐹 𝐴1 1 22 1  Law of Communicating Vessels The pressure at the same depth does not depend on the shape of the vessel, therefore in connected vessels, the surface of the liquid is at the same level. p - p 0 = ρ gh 23 Measuring Pressure The pressure in a fluid is measured with a pressure gauge. Many pressure gauges, such as tire gauges and the gauges on air tanks, measure not the actual or absolute pressure p but what is called gauge pressure. The simplest pressure gauge is the open tube manometer. The pressure measured at the same level must be equal: 24 Measuring Pressure Another common pressure gauge is the mercury barometer. 𝑝 𝑎𝑡𝑚 = 𝑝 = 𝜌𝑔; 𝑦2 − 𝑦1 = 𝜌𝑔ℎ The mercury barometer reads the atmospheric pressure 𝑝 𝑎𝑡𝑚 directly from the height of the mercury column. Pressures are often described in terms of the height of the corresponding mercury column, as so many “millimeters of mercury” (abbreviated mm Hg). A pressure of 1 mm Hg is called 1 torr, after Evangelista Torricelli, inventor of the mercury barometer. 25  Buoyancy A body immersed in water seems to weigh less than when it is in air. When the body is less dense than the fluid, it floats. The human body usually floats in water, and a helium-filled balloon floats in air. These are examples of buoyancy, a phenomenon described by Archimedes’s principle: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. 𝐹𝐵 = 𝜌𝑓𝑉𝑓𝑔 26 Center of Buoyancy o The force of buoyancy acts at the center of mass of the missing fluid. o The displacing object has a center of gravity at its center of mass. o The two forces may not act at the same point. 27 Buoyancy o An object in a fluid displaces a volume that had some mass. o If the object is heavier than the fluid it sinks. o If the object is lighter it rises. Fnet  Vg  mg a  ( Vg  mg ) / m o An object suspended in a fluid has less apparent weight due to buoyancy. 28  Surface Tension An object less dense than water, such as an air-filled beach ball, floats with part of its volume below the surface. Conversely, a paper clip can rest atop a water surface even though its density is several times that of water. This is an example of surface tension. The surface of the liquid behaves like a membrane under tension. 29  Surface Tension o Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible. o Surface tension σ is the contractile force which always exists in the boundary between two phases at equilibrium o At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). o The surface tension force F is proportional to the number of molecules in the area contour length, which is proportional to the surface contour length L 𝐹 𝜎= 𝐿 30  Wetting and capillary phenomena o Why is the height of the liquid in the tubes not the same? When the dimensions of the vessel in which contains the liquid, is close to the radius of curvature of the liquid surface, such vessels are called capillary. 31 Wetting and capillary phenomena The capillary rise of a liquid in a narrow cylindrical capillary is equal to: 2𝜎𝑐𝑜𝑠𝜃 ℎ= ρ𝑔𝑟0 Here r 0 is the radius of the capillary ,  - liquid contact angle, g – free fall acceleration,  - liquid surface tension coeficient, ρ – density of the liquid, r - is the radius of curvature of the meniscus. 32 Wetting and capillary phenomena High wetting liquid 2𝜎 ℎ= ρ𝑔𝑟0 Low wetting liquid 33 Wetting and Spreading The spreading parameter S is given by If S < 0, partial wetting is said to occur, with a finite contact angle. 𝑆 = 𝜎𝑆𝐺 − 𝜎𝑆𝐿 + 𝜎𝐿𝐺 If the contact angle is 180o, the liquid This coefficient determines whether a droplet forms a complete sphere and the forms, or the surface is completely wetted. liquid is non-wetting. It is a measure of the difference in surface energy between the substrate dry and wet. Non-wetting If S > 0, the liquid spreads completely to cover the surface and lower its surface energy:  is zero. In general, liquids will spread on highly polarizable substrates such as metal and glass. Wetting layer They may or may not on plastics – if the liquid is less polarizable than the substrate it will. 34  Measuring Surface Tension Measuring the contact angle is obviously a Roughness: If the surface is rough, good way of determining the surface energy of then the local contact angle and the a liquid on a particular substrate, if the other macroscopic (measured) contact angle surface energy terms are known. will differ. This is a very hard problem A goniometer can be used to measure the to deal with, both theoretically and angle accurately, or photographs taken on experimentally. which measurements are made. If the droplet grows, the advancing and However, there are experimental difficulties to receding angles will differ due to take into account. hysteresis effects. These are also not well understood. In general the advancing angle is used, although sometimes both are quoted. Molten polymer on substrate Surface cleanliness is a major issue. Finger grease, for instance, can completely change the measurements.  35 Hydrophobic and Hydrophilic Surfaces Hydrophobic surfaces are obviously ones that repel water whereas hydrophilic ones are covered with a wetting layer. Different applications have different requirements. Hydrophobic surfaces Hydrophilic surfaces Leaves, duck feathers etc are Contact lenses must be made designed so that water rapidly forms out of materials that favour droplets and rolls off them wetting, and prevent the lens ('water off a duck's back'). adhering to the cornea. Aircraft are sprayed with a hydrophobic In many industrial processes liquid so that a continuous film of water such as paper coating, wetting does not form which can transform into must be achieved very fast to solid ice during flight, substantially cope with the speed of the increasing weight. process (m's per second). Teflon frying pans and saucepans are Likewise with adhesives need a used to prevent most things – not just continuous film to form to give water – sticking. Made from good adhesive strength. polytetrafluorine ethylene (PTFE). 36  Fluid Dynamics Fluid motion (flow) can be extremely complex. Some situations can be represented by simple idealized models. A fluid can be considered ideal if o The fluid is incompressible. o The fluid is nonviscous (analogous to friction-free motion). o The flow is laminar. The model fails if the fluid has significant viscosity and the flow is turbulent rather than laminar. Viscosity - a fluid’s resistance to flow. Laminar flow occurs when the fluid velocity at each point in the fluid is constant. The flow is smooth; it doesn’t change or fluctuate. 37  Fluid Dynamics The path of an individual particle in a moving fluid is called a flow line. If the overall flow pattern does not change with time, the flow is called steady flow. In a laminar flow, adjacent layers of fluid slide smoothly past each other and the flow is steady. At sufficiently high flow rates, or when boundary surfaces cause abrupt changes in velocity, the flow can become irregular and chaotic. This is called turbulent flow. 38  Continuity Equation The mass of a moving fluid doesn’t change as it flows. This leads to an important quantitative relationship called the continuity equation. 𝐴1𝑣1 = 𝐴 2 𝑣 2 The product 𝐴𝑣 is the volume flow rate 𝑑𝑉/𝑑𝑡, the rate at which volume crosses a section of a tube 𝑑𝑉 = 𝐴𝑣 𝑑𝑡 The flow speed changes as the streamlines get closer together or farther apart. Flow is faster in narrower parts of a tube, slower in wider parts. 39  Bernoulli’s Equation Bernoulli’s equation relates the pressure, flow speed, and height for flow of an ideal, incompressible fluid. It is an essential tool in analysing plumbing systems, hydroelectric generating stations, and the flight of airplanes. We need to apply work-energy theorem to derive the relation: 𝑊𝑡𝑜𝑡 = Δ𝑊𝐾 + Δ𝑈𝑔𝑟𝑎𝑣 Taking into account that only nongravitational forces do work on the fluid element, the net work done on the element by the surrounding fluid during the displacement is 𝑑𝑊 = 𝑝 𝐴 𝑑𝑠 − 𝑝 𝐴 𝑑𝑠 = 𝑝 − 𝑝 𝑑𝑉 1 1 1 2 2 2 1 2 40 Bernoulli’s Equation The net change in kinetic energy dWK during time dt is 1 𝑑𝑊𝐾 = 𝜌𝑑𝑉 𝑣22 − 𝑣 12 2 The net change in potential energy during time dt is 𝑑𝑈𝑔𝑟𝑎𝑣 = 𝜌𝑑𝑉𝑔 𝑦2 − 𝑦1 Combining equations together, we obtain 1 𝑝1 − 𝑝2 𝑑𝑉 = 𝜌𝑑𝑉 𝑣22 − 𝑣 12 + 𝜌𝑑𝑉𝑔 𝑦2 − 𝑦1 2 1 𝑝1 − 𝑝2 = 𝜌 𝑣22 − 𝑣 21 + 𝜌𝑔 𝑦2 − 𝑦1 2 Bernoulli’s equation 41 Bernoulli’s Equation Bernoulli’s equation states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow. 1 𝑝1 − 𝑝2 = 𝜌 𝑣22 − 𝑣 21 + 𝜌𝑔 𝑦2 − 𝑦1 2 1 𝜌 𝑣22 − 𝑣 21 - shows the pressure difference associated with 2 the change of speed of the fluid. 𝜌𝑔 𝑦2 − 𝑦1 - additional pressure difference caused by the weight of the fluid and the difference in elevation of two ends. 1 2 1 2 𝑝1 + 𝜌𝑔𝑦1 + 𝜌𝑣1 = 𝑝 2 + 𝜌𝑣2 + 𝜌𝑔𝑦 2 2 2 42  Viscosity of liquids Assume that the liquid is made up of separate layers of liquid. Internal friction forces acting in the tangential direction to the surfaces of the layers occur between fluid layers moving at different velocities: a) the faster moving layer exerts an accelerating force on the slower moving one, b) the slower moving layer exerts a braking force on the slower moving layer The layers moving in this way are observed as the liquid flows through the 43 wetted tube. Outline o Fluid mechanics Fluids; Quantities describing fluids (density, volume, pressure); Fluid dynamics. o Thermodynamics Macroscopic description of matter; Temperature; Heat. o Summary; o Next lecture. 44  Macroscopic Description of Matter Macroscopic properties, such as pressure and temperature, have their basis in the microscopic motions of atoms and molecules, and it is important to explore this micro/macro connection. Each of the elements and most compounds can exist as a solid, liquid, or gas – the three most common phases of matter. The change between liquid and solid (freezing or melting) or between liquid and gas (boiling or condensing) is called a phase change. 45 Macroscopic Description of Matter A solid is a rigid macroscopic system consisting of particle-like atoms connected by spring-like molecular bonds. Solids are nearly incompressible. A liquid is a system in which the molecules are loosely held together by weak molecular bonds. Like a solid, a liquid is nearly incompressible. A gas is a system in which each molecule moves through space as a free, noninteracting particle until, on occasion, it collides with another molecule or with the wall of the container. Gas is highly compressible. 46 Macroscopic Description of Matter The parameters used to characterize or describe a macroscopic system are known as state variables (mass density, volume, pressure, mass, thermal energy) because, taken all together, they describe the state of the macroscopic system. The mass of a macroscopic system is directly related to the total number of atoms or molecules in the system, denoted N (number without units). A typical macroscopic system has 𝑁~1025 atoms. Number density 𝑁/𝑉 characterizes how densely the atoms are packed together within the system. The value of 𝑁/𝑉 in a uniform system is independent of the volume V. 47  Mass The atomic mass scale is established by defining the mass of 12C to be exactly 12 u, where u is the symbol for the atomic mass unit. For molecules, the molecular mass is the sum of the atomic masses of the atoms forming the molecule (𝑚 ( O2) = 32 u). The amount of substance can be given in moles instead of mass. 1 mole of substance (1 mol), is 6.02 × 1023 basic particles. The number of basic particles per mole of substance is called Avogadro’s number, 𝑁𝐴 = 6.02 × 1023mol−1. Moles of substance: 𝑛= 𝑁 𝑁𝐴 48  Temperature Temperature is a measure of relative hotness or coldness. Heat is the net energy transferred from one object to another due to a temperature difference. This energy may contribute to the total internal energy of the object, or it may do work, or both. A higher temperature does not necessarily mean that one object has more internal energy than another; the size of the object matters as well. When heat is transferred from one object to another, they are said to be in thermal contact. Two objects in thermal contact without heat transfer are in thermal equilibrium. 49 Temperature A thermometer needs a temperature scale to be a useful measuring device. In 1742, the Swedish astronomer Anders Celsius sealed mercury into a small capillary tube and observed how it moved up and down the tube as the temperature changed. We have Celsius scale, where 0 and 100 degrees correspond to the freezing and boiling point of pure water respectively. The units of the Celsius temperature scale are “degrees Celsius”, °C. The Fahrenheit scale, still widely used in the United States, is related to the Celsius scale by 9 𝑇𝐹 = 𝑇𝐶 + 32° 5 50 3 Temperature The temperature at which all motion would cease, and at which 𝐸𝑡ℎ = 0, is called absolute zero, 𝑇0 = −273°C. Because temperature is related to thermal energy, absolute zero is the lowest temperature that has physical meaning. Temperature scale with the zero point at absolute zero is called an absolute temperature scale. The absolute temperature scale having the same unit size as the Celsius scale is called the Kelvin scale. It is the SI scale of temperature. The units are kelvins (K). 𝑇𝐾 = 𝑇𝐶 + 273.15 51 Zeroth Law of Thermodynamics If C is initially in thermal equilibrium with both A and B, then A and B are also in thermal equilibrium with each other. This result is called the zeroth law of thermodynamics. Two systems are in thermal equilibrium if and only if they have the same temperature. A thermometer actually measures its own temperature, but when a thermometer is in thermal equilibrium with another body, the temperatures must be equal. When the temperatures of two systems are different, they cannot be in thermal equilibrium. 52 Thermal Expansion Most materials expand when their temperatures increase. The change of rod’s length Δ𝐿 (linear expansion) with the temperature change Δ𝑇: Δ𝐿 = 𝛼𝐿0Δ𝑇 If a body has length 𝐿0 at temperature 𝑇0 , then its length L at a temperature 𝑇 = 𝑇0 + Δ𝑇: 𝐿 = 𝐿0 + Δ𝐿 = 𝐿0 + 𝛼𝐿0Δ𝑇 = 𝐿0(1 + 𝛼Δ𝑇) The constant 𝛼, which describes the thermal expansion properties of a particular material, is called the coefficient of linear expansion. The units of 𝛼 are K-1 or (C°)-1. 53  Thermal Expansion Increasing temperature usually causes increases in volume for both solid and liquid materials. Experiments show that if the temperature change Δ𝑇 is not too great (< 100C°), the increase in volume Δ𝑉 : Δ𝑉 = 𝛽𝑉0Δ𝑇 The constant 𝛽 (coefficient of volume expansion) characterizes the volume expansion properties of a particular material. The units of 𝛽 are K-1 or (C°)-1. 𝛽 = 3𝛼 54  Expanding Holes and Volume Expansion If an object has a hole in it, the hole also expands with the object, as shown. The hole does not shrink. The change in volume due to thermal expansion is given by V  V0 T where β is the coefficient of volume expansion and is equal to 3α. 55  Heat Energy transfer that takes place solely because of a temperature difference is called heat flow or heat transfer, and energy transferred in this way is called heat. The temperature rise is directly proportional to the amount of work done (i.e. by vigorous spinning). The unit of heat – calorie (cal) – is defined as the amount of heat required to raise the temperature of 1 gram of water from 14.5°C to 15.5°C. 1cal = 4.186 J. The calorie is not a fundamental SI unit. To be more precise – use joules, as heat is a form of energy. 56 Heat The quantity of heat (𝑄) required to increase the temperature of a mass m of a certain material from T1 to T2 is found to be approximately proportional to the temperature change and mass: 𝑄 = 𝑚𝑐Δ𝑇 Here c is a quantity different for different materials, called the specific heat of the material. For an infinitesimal temperature change dT and corresponding quantity of heat dQ, 1 𝑑𝑄 𝑑𝑄 = 𝑚𝑐𝑑𝑇 𝑐= 𝑚 𝑑𝑇 Q (or dQ) and Δ𝑇 (or dT) can be either positive or negative. When they are positive, heat enters the body and its temperature increases; when they are negative, heat leaves the body and its temperature decreases. 57 Molar Heat Capacity Sometimes it’s more convenient to describe a quantity of substance in terms of the number of moles n rather than the mass m of material. The total mass of material 𝑚 = 𝑛𝑀 𝑄 = 𝑚𝑐Δ𝑇 𝑄 = 𝑛𝑀𝑐Δ𝑇 The product Mc is called the molar heat capacity (or molar specific heat) and is denoted by C. 𝑄 = 𝑛𝐶Δ𝑇 1 𝑑𝑄 𝐶= = 𝑀𝑐 𝑛 𝑑𝑇 58  Phase Changes Phase term is used to describe a specific state of matter, such as a solid, liquid, or gas. A transition from one phase to another is called a phase change or phase transition. Melting occurs when the thermal energy gets so large that molecular bonds begin to break, allowing the atoms to move around. The heat required per unit mass to change its phase is called the heat fusion, denoted Lf. To melt (or freeze) a mass m of material that has a heat of fusion Lf requires a quantity of heat Q given by 𝑄 = ±𝑚𝐿𝑓 59  Phase Changes The temperature at which a solid becomes a liquid or, if the thermal energy is reduced, a liquid becomes a solid is called the melting point or the freezing point. Melting and freezing are phase changes. A system at the melting point is in phase equilibrium, meaning that any amount of solid can coexist with any amount of liquid. The temperature at which a gas becomes a liquid or, if the thermal energy is increased, a liquid becomes a gas is called the condensation point or the boiling point. 60  Heat Transfer The three mechanisms of heat transfer: o Conduction occurs within a body or between two bodies in contact. o Convection depends on motion of mass from one region of space to another. o Radiation is heat transfer by electromagnetic radiation, such as sunshine, with no need for matter to be present in the space between bodies. 61  Conduction On the atomic level, the atoms in the hotter regions have more kinetic energy, on the average, than their cooler neighbours. Metals are good conductors due to “free” electrons. Heat transfer occurs only between regions that are at different temperatures, and the direction of heat flow is always from higher to lower temperature. 62 Conduction The heat current (rate of heat flow) is 𝑑𝑄 𝑇𝐻 − 𝑇𝐶 𝐻= = 𝑘𝐴 𝑑𝑡 𝐿 k is thermal conductivity of the material. The quantity 𝑇𝐻 − 𝑇𝐶 /𝐿 is the temperature gradient per unit length; it is called the magnitude of the temperature gradient. Materials with large k are good conductors of heat; materials with small k are poor conductors, or insulators. The SI units of heat current H are units of energy per time (W). The units of k are W/m ∙ K. 63  Conduction For thermal insulation in buildings, engineers use the concept of thermal resistance, denoted by R. The thermal resistance R of a slab of material with area A is defined so that the heat current H through the slab is 𝐴(𝑇𝐻 − 𝑇𝐶 ) 𝐻= 𝑅 𝐿 𝑅= 𝑘 L is the thickness of the slab. The Si unit of R is 1m2 ∙ K/W. Common practice in new construction in severe northern climates is to specify R values of around 30 for exterior walls 64 and ceilings.  Convection Convection is the transfer of heat by mass motion of a fluid from one region of space to another. If the fluid is circulated by a blower or pump, the process is called forced convection; if the flow is caused by differences in density due to thermal expansion, such as hot air rising, the process is called natural convection or free convection. 65 Radiation Radiation is the transfer of heat by electromagnetic (EM) waves such as visible light, infrared, and ultraviolet radiation. Every body, even at ordinary temperatures, emits energy in the form of EM radiation. The rate of energy radiation from a surface is proportional to the surface area and to the power of the absolute (Kelvin) temperature T. The rate also depends on the nature of the surface; this dependence is described by a quantity e called the emissivity. 𝐻 = 𝐴𝑒𝜎𝑇4 𝜎 is a fundamental physicalconstant called the Stefan- Boltzmann constant. 𝜎 = 5.670400(40) × 10−8 W/m2 ∙ K 4 66 Summary o Density is mass per unit volume. o Pressure is normal force per unit area. Absolute pressure is the total pressure in a fluid; gauge pressure is the difference between absolute pressure and atmospheric pressure. o An ideal fluid is incompressible and has no viscosity. Conservation of mass in an incompressible fluid is expressed by the continuity equation. Bernoulli’s equation can be used to relate the properties of the flow at any two points. o Two bodies in thermal equilibrium must have the same temperature (Celsius, Fahrenheit, Kelvin scales). o Heat is energy in transit from one body to another as a result of a temperature difference. o Transfer of heat: conduction, convection, radiation. 67 Next Lecture Laws of Thermodynamics 68