HeatHeat is a shortened way of saying "heat energy." When something's hot, it has a lot of heat energy; when it's cold, it has less. But even things that seem cold (such as polar bears and icebergs) have rather more heat energy than you might suppose.Objects can store heat because theatomsand molecules inside them are jostling around and bumping into one another like people in a crowd. This idea is called the kinetic theoryof matter, because it describes heat as a kind ofkinetic energystored by the atoms and molecules from which materials are made. It was developed in the 19th century by various scientists, including Austrian physicist Ludwig Boltzman (18441906) and British physicist James Clerk Maxwell (18311879).The kinetic theory helps us understand where the energy goes when we heat something up. If you put a pan full of coldwateron a hot stove, you're going to make the molecules in the water move around more quickly. The more heat you supply, the faster the molecules move and the further apart they get. Eventually, they bump around so much that they break apart from one another. At that point, theliquidyou've been heating turns into a gas: your water becomes steam and starts evaporating away.What happens when something has no heat at all?Now suppose we try the opposite trick. Let's take a jug of water and put it in therefrigeratorto cool it down. A refrigerator works by systematically removing heat energy from food. Put water inside a refrigerator and it immediately starts to lose heat energy. The more heat it loses, the more kinetic energy its molecules lose, the more slowly they move, and the closer they get. Soon or later, they get close enough to lock together in crystals; the liquid turns to solid; and you find yourself with a jug of ice!But what if you have a super-amazing refrigerator that keeps on cooling the water so it gets colder... and colder... and colder. A home freezer, if you have one, can take the temperature down to somewhere between 10C and 20C (14F to 4F). But what if you keep on cooling lower than that, taking away even more heat energy? Eventually, you'll reach a temperature where the water molecules pretty much stop moving altogether because they have absolutely no kinetic energy left. For reasons we won't go into here, this magic temperature is 273.15 C (459.67F) and we refer to it asabsolute zero.

In theory, absolute zero is the lowest temperature anything can ever reach. In practice, it's virtually impossible to cool anything down that muchscientists have tried very hard but still not actually reached such a low temperature. Amazing things happen when you get close to absolute zero. Some materials, for example, can lose virtually all theirresistanceand become amazing conductors ofelectricitycalledsuperconductors. There's a great PBS website where you can find out lots more aboutabsolute zeroand the remarkable things that happen there.What's the difference between heat and temperature?Now you know about absolute zero, it's easy to see why something like an iceberg (which could be at the chilly temperature of about 3-4C or round about 40F) is relatively hot. Compared to absolute zero, everything in our everyday world is hot because its molecules are moving around and they have at leastsomeheat energy. Everything around us is also at a much hotter temperature than absolute zero.You can see there's a close link between how much heat energy something has and its temperature. So are heat energy and temperature just the same thing? No! Let's get this clear: Heatis the energy stored inside something. Temperatureis a measurement of how hot or cold something is.An object's temperature doesn't tell us how much heat energy it has. It's easy to see why not if you think about an iceberg and an ice cube. Both are at more or less the same temperature but because the iceberg has far more mass than the ice cube, it contains billions more molecules and a great deal more heat energy.How can we measure temperature?We measure temperature withthermometersusing two common (and fairly arbitrary) scales calledCelsius(or centigrade) andFahrenheit, named for Swedish astronomer Anders Celsius (17011744) and German physicist Daniel Fahrenheit (16861736).There's also a scientific temperature scale called the Kelvin(or absolute scale), named for British physicist William Thompson (later Lord Kelvin, 18241907). Logically, the Kelvin scale makes much more sense to scientists because it runs upward from absolute zero (which is also known as 0K, without a degree symbol between the zero and the K). You'll see lots of Kelvin temperatures in physics, but you won't find weather forecasters giving you temperatures that way. For the record, a reasonably hot day (2030C) comes in at something like 290300K: you just add 273 to your Celsius figure to convert to Kelvin.How does heat travel?One thing you've probably noticed about heat is that it doesn't generally stay where you put it. Hot things get colder, cold things get hotter, andgiven enough timemost things eventually end up the same temperature. How come?There's a basic law of physics called thesecond law of thermodynamicsand it says, essentially, that cups of coffee always go cold and ice creams always melt: heat flows from hot things toward cold ones and never the other way around. You never see coffee boiling all by itself or ice creams getting colder on sunny days! The second law of thermodynamics is also responsible for the painful fuel bills that drop through your letterbox several times a year. In short: the hotter you make your home and the colder it is outside, the more heat you're going to lose. To reduce that problem, you need to understand the three different ways in which heat can travel: called conduction, convection, and radiation. Sometimes you'll see these referred to as three forms ofheat transfer.ConductionConduction is how heat flows between twosolidobjects that are at different temperatures and touching one another (or between two parts of the same solid object if they're at different temperatures). Walk on a stone floor in your bare feet and it feels cold because heat flows rapidly out of your body into the floor by conduction. Stir a saucepan of soup with a metal spoon and you'll soon have to find a wooden one instead: heat travels rapidly along the spoon by conduction from the hot soup into your fingers.ConvectionConvection is the main way heat flows through liquids and gases. Put a pan of cold, liquid soup on your stove and switch on the heat. The soup in the bottom of the pan, closest to the heat, warms up quickly and becomes less dense (lighter) than the cold soup above. The warmer soup rises upward and colder soup up above it falls down to take its place. Pretty soon you've got a circulation of heat running through the pan, a bit like an invisible heat conveyor, with warming, rising soup and cooling, falling soup. Gradually, the whole pan heats up. Convection is also one of the ways our homes heat up when we turn on the heating. Air warms up above the heaters and rises into the air, pushing cold air down from the ceiling. Before long, there's a circulation going on that gradually warms up the entire room.RadiationRadiation is the third major way in which heat travels. Conduction carries heat through solids; convection carries heat through liquids and gases; but radiation can carry heat through empty spaceeven through a vacuum. We know that much simply because we're alive: almost everything we do on Earth is powered by solar radiation beamed toward our planet from the Sun through the howling empty darkness of space. But there's plenty of heat radiation on Earth too. Sit near a crackling log fire and you'll feel heat radiating outward and burning your cheeks. You're not in contact with the fire, so the heat's not coming to you by conduction and, if you're outside, convection probably isn't carrying much toward you either. Instead, all the heat you feel travels by radiationin straight lines, at the speed oflightcarried by a type ofelectromagnetismcalledinfraredradiation.Why do some things take longer to heat up than others?Different materials can store more or less heat depending on their internal atomic or molecular structure. Water, for example, can store huge amounts of heatthat's one of the reasons we use it incentral-heating systemsthough it also takes a relatively long time to heat up.Metalslet heat pass through them very well and heat up quickly, but they're not so good at storing heat. Things that store heat well (like water) are said to have a highspecific heat capacity.The idea of specific heat capacity helps us understand the difference between heat and temperature in another way. Suppose you place an emptycoppersaucepan on top of a hot stove that's a certain temperature. Copper conducts heat very well and has a relatively low specific heat capacity, so it heats up and cools down extremely quickly (that's why cooking pots tend to have copper bottoms). But if you fill the same pan with water, it takes far longer to heat up to the same temperature. Why? Because you need to supply much more heat energy to raise the temperature of the water by the same amount. Water's specific heat capacity is roughly 11 times higher than copper's, so if you have the same mass of water and copper, it takes 11 times as much energy to raise the temperature of the water by the same number of degrees.Specific heat capacities can help you understand what happens when you heat your home in different ways in winter-time. Air heats up relatively quickly for two reasons: first, because the specific heat capacity of air is about a quarter of water's; second, because air is a gas, it has relatively little mass. If your room is freezing and you turn on a fan (convection) heater, you'll find everythingseemsto warm up very quickly. That's because you're essentially just heating up the air. Turn off the fan heater and the room will cool down pretty fast too because the air, by itself, doesn't have much ability to store heat.So how do you get your room really warm? Don't forget that there isn't just air in it that you need to heat up: there's solid furniture, carpets, curtains, and lots of other things too. It takes much longer to heat these things up because they're solid and much more massive than the air. The more cold, solid objects you have in your room, the more heat energy you have to supply to heat them all up to a particular temperature. You'll need to heat them up using conduction and radiation as well as convectionand that takes time. But, because solid things store heat well, they also take time to cool down. So, providing you have decent insulationto stop heat escaping from the walls, windows, and so on, once your room has reached a certain temperature, it should stay warm for some time without your having to add any more heat.Latent heatDoes more heat always make higher temperature? From what we've said so far, you might be forgiven for thinking that giving something more heat always makes its temperature rise. Generally that's true, but not always.Suppose you have a lump of ice floating in a pan of water and you place it on your hot stove. If you stick a thermometer in the ice-water mixture, you'll find it's around 0C (32F)the normal freezing point of water. But if you keep heating, you'll find the temperature stays the same until pretty much all the ice has melted, even though you're supplying more heat all the time. It's almost as though the ice-water mixture is taking the heat you're giving it and hiding it away somewhere. Oddly enough, that's exactly what's happening!

When a substance changes from solid to liquid or from liquid to gas, it takes energy to change its state. To turn solid ice into liquid water, for example you have to push the water molecules inside further apart and break apart the framework (or crystalline structure) that holds them together. So while ice is melting (in other words, during the change of state from solid water to liquid ice), all the heat energy you supply is being used to separate molecules and none is left over for raising the temperature.The heat needed to change a solid into a liquid is called thelatent heat of fusion. Latent means hidden and "latent heat of fusion" refers to the hidden heat involved in making a substance change state from solid to liquid or vice-versa. Similarly, you need to supply heat to change a liquid into a gas, and this is called thelatent heat of vaporization.Latent heat is a kind of energy and, although it may seem to be "hidden," it doesn't vanish into thin air. When liquid water freezes and turns back to ice, the latent heat of fusion is given off again. You can see this if you cool water systematically. To start with, the temperature of the water falls regularly as you remove heat energy. But at the point where liquid water turns to solid ice, you'll find water freezes without getting any colder. That's because the latent heat of fusion is being lost from the liquid as it solidifies and it's stopping the temperature from falling so quickly.

Temperature DefinedTemperatureis a measure of how hot or cold something is; specifically, a measure of the averagekinetic energyof the particles in an object, which is a type of energy associated with motion. But how hot is hot, and how cold is cold? The terms hot and cold are not very scientific terms. If we really want to specify how hot or cold something is, we must use temperature. For instance, how hot is melted iron? To answer that question, a physical scientist would measure the temperature of the liquid metal. Using temperature instead of words, like hot or cold, reduces confusion.Temperature Depends on the Kinetic Energy of ParticlesAll matter is made of particles - atoms or molecules - that are in constant motion. Because the particles are in motion, they have kinetic energy. The faster the particles are moving, the more kinetic energy they have. What does temperature have to do with kinetic energy? Well, as described in this figure, the more kinetic energy the particles of an object have, the higher is the temperature of the object.

Temperature is an average measure. Particles of matter are constantly moving, but they don't all move at the same speed and in the same direction all the time. As we can see in this figure, the motion of the particles is random. The particles of matter in an object move in different directions, and some particles move faster than others. As a result, some particles have more kinetic energy than others. So what determines an object's temperature? An object's temperature is the best approximation of the kinetic energy of the particles. When we measure an object's temperature, we measure the average kinetic energy of the particles in the object.The higher the temperature, the faster the molecules of the substance move, on the average. Dyes will spread more rapidly through hot water than cold water. This is because of the increased motion of the molecules. Temperature does not have to do with the number of molecules involved. Under given conditions, the temperatures of 10-ml and 100-ml samples of boiling water are equal. This means that the average kinetic energy of the molecules is the same for the two different quantities of water.

In this image, there is more tea in the teapot than in the mug, but the temperature of the tea in the mug is the same as the temperature of the tea in the teapot.Measuring TemperatureSince molecules are so small, you must use an indirect method to measure the kinetic energy of the molecules of a substance. As heat is added to a substance, the molecules move more rapidly. This increased motion causes a small increase in the volume, or amount of space, taken up by most materials. There are devices that use the expansion of a substance to give an indirect measure of temperature. Such devices are calledthermometers.There are many types of thermometers. Many thermometers are thin glass tubes filled with a liquid. Mercury and alcohol are often used in thermometers because they remain liquids over a large temperature range. A change in temperature causes a small change in the volume of the liquid. However, this effect is magnified when the liquid expands in the very thin tube of the thermometer.

Thermometer

Some thermometers involve the use of bimetal strips. In such thermometers, strips made of two different metals are bonded or glued together. Because the metals expand at different rates, the combined strip bends in a certain direction when it is heated. When it cools, it bends in the opposite direction. The figure below shows a bimetal strip used as a thermostat. Athermostatis a device used to control heating and cooling systems.

Thermostat

Some thermometers, often used on the outside of aquariums, contain liquid crystals that change color based on temperature. As temperature increases, the molecules of the liquid crystal bump into each other more and more. This causes a change in the structure of the crystals, which in turn affects their color. These thermometers are able to accurately determine the temperature between 65 F and 85 F.

A thermometer with no marks, or graduations, would not be very useful to you. A thermometer is calibrated by marking two fixed points. The space between these fixed points is broken up into divisions called degrees. Degrees are used to indicate temperature. There are three types of temperature scales commonly used today: Celsius, Fahrenheit and Kelvin. We are used to expressing temperature with degrees Fahrenheit (F). Scientists often use degrees Celsius (C), but the Kelvin (K) is the SI unit for temperature.Thermometers can measure temperature because of thermal expansion.Thermal expansionis the increase in volume of a substance due to an increase in temperature. As a substance gets hotter, its particles move faster. The particles themselves do not expand; they just spread out so that the entire substance expands. Different substances expand by different amounts for a given temperature change. When you insert a thermometer into a hot substance, the liquid inside the thermometer expands and rises. You measure the temperature of a substance by measuring the expansion of the liquid in the thermometer.

Thermal and Kinetic EnergyAtoms are always in motion. Imagine you had a microscope powerful enough to see individual molecules in a compound (or atoms in case of an element). You would see that the molecules are in constant motion, even in a solid object. In a solid, the molecules are not fixed in place, but act like they are connected by springs as shown here.

Molecules in solid

Each molecule stays in the same average place, but constantly jiggles back and forth in all directions. As you might guess, the 'jiggling' means motion, and motion means energy. This 'jiggling' is caused by thermal energy, which is a kind of kinetic energy.

Displacement (symbolizeddors), also called length or distance, is a one-dimensional quantity representing the separation between two defined points. The standard unit of displacement in the International System of Units (SI) is themeter(m).DisplacementAdisplacementis the shortestdistancefrom the initial to the finalpositionof a point P.[1]Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A "displacement vector" represents the length and direction of that imaginary straight path.Aposition vectorexpresses the position of a point P in space in terms of a displacement from an arbitrary reference point O (typically the origin of a coordinate system). Namely, it indicates both the distance and direction of an imaginary motion along a straight line from the reference position to the actual position of the point.A displacement may be also described as a 'relative position': the final position of a point (Rf) relative to its initial position (Ri), and a displacement vector can be mathematically defined as thedifferencebetween the final and initial position vectors:

In considering motions of objects over time the instantaneousvelocityof the object is the rate of change of the displacement as a function of time. The velocity then is distinct from the instantaneousspeedwhich is the time rate of change of the distance traveled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalently a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be 'fixed in space' (such as, for instance, a point fixed on the floor of the train station).For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. (Note that the averagevelocity, as a vector, differs from theaverage speedthat is the ratio of the path lengtha scalarand the time interval.)

Sample Problem Solving:

An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure below.

a) Find the distance covered by the moving object.

b) Find the magnitude and direction of the displacement of the object.

Solution to Problem 1:a) distance = AB + BC + CB + BC = 5 + 4 + 4 + 4 = 17 kmb) The magnitude of the displacement is equal to the distance between the final point C and the initial point A = AC = 9 kmThe direction of the displacement is the direction of the ray AB.

AccelerationAcceleration, inphysics, is therateat which thevelocityof an object changes over time. An object's acceleration is the net result of any and allforcesacting on the object, as described byNewton's Second Law.TheSIunit for acceleration is themetre per second squared(m/s2). Accelerations arevector quantities (they havemagnitudeanddirection) and add according to theparallelogram law.As avector, the calculated netforceis equal to the product of the object's mass (ascalarquantity) and the acceleration.For example, when a car starts from a standstill (zero relative velocity) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car turns there is an acceleration toward the new direction. For this example, we can call the accelerating of the car forward a "linear acceleration", which passengers in the car might experience as force pushing them back into their seats. When changing directions, we might call this "non-linear acceleration", which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the opposite direction of the direction of the vehicle, sometimes calleddeceleration.Passengers may experience deceleration as a force lifting them away from their seats. Mathematically, there is no separate formula for deceleration, as both are changes in velocity. Each of these accelerations (linear, non-linear, deceleration) might be felt by passengers until their velocity and direction match that of the car.Sample Problem Solving:What is the acceleration of an object that moves with uniform velocity?Solution:

If the velocity is uniform, let us say V, then the initial and final velocities are both equal to V and the definition of the acceleration givesaverage acceleration = V - Vt - t0= 0

The acceleration of an object moving at a constant velocity is equal to 0.PressurePressure is force per unit area applied in a directionperpendicularto the surface of an object.Gauge pressure(also spelledgagepressure)[a][not in citation given]is the pressure relative to the local atmospheric or ambient pressure. Pressure is measured in any unit of force divided by any unit of area. TheSIunit of pressure is thenewtonpersquare metre, which is called thepascal(Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. Thelbf/square inch(PSI) is the traditional unit of pressure in US/UK customary units. A pressure of 1Pa approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1kPa =1000Pa) 1kPa is approximately one-seventh of a lbf/in2..Sample Problem Solving:Determine the mass of the Earth's atmosphere.solutionSince pressure is force divided by area, the force of the atmosphere pressing on the surface of the earth can be found by multiplying standard atmospheric pressure by the surface area of the earth. Given that the force of an object's weight is its mass times the acceleration due to gravity, the mass of the earth's atmosphere is the force it exerts divided by the acceleration due to gravity. Or symbolicallyF=PA=P(4r2)=W=mg

m=W=P(4r2)=(101,325Pa)(4)(6.37106m)2

gg9.8m/s2

m=5.271018kg

ForceInphysics, aforceis any interaction which tends to change the motion of an object.[1]In other words, a force can cause an object withmassto change itsvelocity(which includes to begin moving from astate of rest), i.e., toaccelerate. Force can also be described by intuitive concepts such as a push or a pull. A force has bothmagnitudeanddirection, making it avectorquantity. It is measured in theSI unitofnewtonsand represented by the symbolF.The original form ofNewton's second lawstates that the net force acting upon an object is equal to therateat which itsmomentumchanges with time. If the mass of the object is constant, this law implies that theaccelerationof an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to themassof the object. As a formula, this is expressed as:

where the arrows imply a vector quantity possessing both magnitude and direction.Related concepts to force include:thrust, which increases the velocity of an object;drag, which decreases the velocity of an object; andtorquewhich produceschanges in rotational speedof an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-calledmechanical stress.Pressureis a simple type of stress. Stress usually causesdeformationof solid materials, or flow influids. VibrationVibrationis a mechanical phenomenon wherebyoscillationsoccur about anequilibrium point. The oscillations may beperiodicsuch as the motion of a pendulum orrandomsuch as the movement of a tire on a gravel road.Vibration is occasionally "desirable". For example, the motion of atuning fork, thereedin awoodwind instrumentorharmonica, ormobile phonesor the cone of aloudspeakeris desirable vibration, necessary for the correct functioning of the various devices.More often, vibration is undesirable, wastingenergyand creating unwantedsoundnoise. For example, the vibrational motions ofengines,electric motors, or anymechanical devicein operation are typically unwanted. Such vibrations can be caused byimbalancesin the rotating parts, unevenfriction, the meshing ofgearteeth, etc. Careful designs usually minimize unwanted vibrations.The study of sound and vibration are closely related. Sound, or "pressurewaves", are generated by vibrating structures (e.g.vocal cords); these pressure waves can also induce the vibration of structures (e.g.ear drum). Hence, when trying to reduce noise it is often a problem in trying to reduce vibration.Sample Problem Solving:Obtain torsional natural frequencies of the system shown in Figure 9.10 using the transfer matrix method. Check results with the closed form solution available. TakeG= 0.8 x 1011N/m2

Figure 9.10 :Solution:We have following properties of the rotor

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