Internal Energy vs. Heat The term heat refers is the energy that is transferred from one body or location due to a difference in temperature. This is similar to the idea of work, which is the energy that is transferred from one body to another due to forces that act between them. Heat is internal energy when it is transferred between bodies. Technically, a hot potato does not possess heat; rather it possesses a good deal of internal energy on account of the motion of its molecules. If that potato is dropped in a bowl of cold water, we can talk about heat: There is a heat flow (energy transfer) from the hot potato to the cold water, the potato's internal energy is decreased, while the water's is increased by the same amount.

Units for Heat Like any type of energy, the SI unit for heat is the Joule. Another common unit is the calorie, which is approximately the amount of heat energy needed to raise one gram one degree Celsius. 1000 calories are in a Calorie, which is used to measure the energy in foods (that the human body can make use of). The British thermal unit (BTU) is approximately the energy needed to raise one pound of water one degree Fahrenheit. 1 cal 4.186J 1 BTU 1055 J 252 cal

Internal vs. "Externa" Energy Suppose a 1 kg block of ice is sliding at 7 m/s. This is the speed of the center of mass of the block, not the speed of each individual water molecule. To calculate the total kinetic energy m = 7 m/s of the water molecules of the block directly, we would have to know the speed of each molecule as it vibrates, all 33.4 trillion trillion of them! (In practice we would just measure the temperature & mass of the ice.) The internal energy of the ice does not depend on the motion of the whole body relative to Earth. What matters is the motion of the molecules in the reference frame of the block. Otherwise, it would be impossible for a cold object to move quickly or a hot one to move slowly. Note: If friction is present, it could do work on the ice and convert some of the "uniform" kinetic energy of the block into "random" kinetic energy of its molecules (internal energy). Regardless, the total energy of the block is the kinetic energy of the center of mass + the internal energy: Kotal omEnt

Temperature vs. Internal Energy Temperature and internal energy are related but not the same thing. Temperature is directly proportional to the average molecular kinetic energy. Note the word average is used, not total Consider a bucket of hot water and a swimming pool full of cold water. The hot water is at a higher temperature, but the pool water actually has more internal energy! This is because, even though the average kinetic energy of the water molecules in the bucket is much greater than that of the pool, there are thousands of times more molecules in the pool, so their total energy is greater It's analogous to this: A swarm of 1000 slow moving bees could have more total kinetic energy than a dozen fast moving, hyperactive bees buzzing around like crazy. One fast bee has more kinetic energy than a slow one, but there are a lot more slow ones. true for gases, approximately true for solids and liquids wh se molecules interact with each other more, contintued on next slide

Temperature vs. Internal Energy (cont.) Which has more internal energy, a bucket of hot water or a bucket of cold water? answer: The bucket of hot water has more internal energy, at least if the buckets contain the same amount of water. Internal energy depends on the amount (mass) of substance and the kinetic energy of the molecules of the substance. Temperature only depends on the molecules' kinetic energy; it is independent of mass.

Temperature Scales Fahrenheit: water freezes at 32 F; boils at 212 oF Celsius: water freezes at 0 C; boils at 100oC Kelvin: water freezes at 273.15 K; boils at 373.15 K A change of 100 C corresponds to a change of 180 F. This means 5C" = 9 Fo or I C 1.8 Fo. Note that the degree symbol is on the opposite side of the letter, indicating that we're talking about temperature differences. In other words, five steps on the Celsius scale is equivalent to nine steps on the Fahrenheit scale, but 5 C is certainly not equal to 9 F. Since these scales are linear, and they're offset by 32 F, we get the conversion formula: F 1.8C32 One step on the Kelvin scale is the same as one step on the Celsius scale. These scales are off by 273.15 K, so: K-C + 273.15 Room temperature is around 293 kelvins, which is 20 C, or 68 F

Absolute Zero & the Kelvin Scale The Kelvin scale is setup so that its zero point is the coldest possible temperature- absolute zero, at which point a substance would have zero internal energy. This is 273.15 C, or -459.69 F. Absolute zero can never be reached, but there is no limit to how close we can get to it. Scientists have cooled substances to within 10-5 kelvins of absolute zero. How do we know how cold absolute zero is, if nothing has ever been at that temperature? The answer is by graphing Pressure vs. Temperature for a variety of gases and extrapolating. A gas exerts no pressure when at absolute zero. gas B gas C T ( C) 273.15 C

ermal Equilibrium Two bodies are said to be at thermal equilibrium if they are at the same temperature. This means there is no net exchange of thermal energy between the two bodies. The top pair of objects are in contact, but since they are at different temps, they are not in thermal equilibrium, and energy is flowing from the hot side to the cold side hot heat cold 26 C 26 C No net heat flow mp and, therefore ar There is no net flow of heat energy here.

Heat Transfer Processes Heat energy can be transferred from one body to another in three different ways. Upcoming slides will give an example of each. Conduction: Energy is transferred when two objects are in direct contact. Molecules of the hotter object bump into molecules of the colder object and cause them to speed up, warming the colder object. . Convection: Energy is transferred from one body to a cooler one via currents in a fluid (a gas or liquid). Radiation: All objects, at any temperature, radiate electromagnetic radiation (light of visible and invisible wavelengths). Unlike conduction & convection, no medium (matter of any type) is necessary for heat transfer through radiation. Objects absorb radiation as well. At thermal equilibrium it will absorb as much as it radiates

Conduction k decides to become a blacksmith. In order to forge a horse- shoe for his horse, Schmedric Bucephalus, Scmedrick heats up the shoe in a fire, pounds on it with a mallet to shape it, and then cools it by dipping it in a bucket of water. Because the water is colder, heat flows from the shoe to the water--quickly at first, and more slowly as the shoe cools. The water molecules, with little kinetic energy, are in direct contact with the iron atoms, which are jiggling rapidly and have lots of kinetic energy. When an iron atom bumps into a water molecule, the iron atom slows down a bit, while the water molecule speeds up (an elastic collision). In this way water gains the heat energy that the iron loses. ,-water molecule iron atom zoomed in view

Convection The water near the hot horseshoe is warmer than the water further from the shoe. This warm water is lower in density than the cooler water, since its molecules are moving faster and taking up more space. With lower density, the warm water begins to float to the surface, carrying its heat energy with it. As it rises to the surface it cools and becomes denser. Then it begins to sink, warmer water from below taking its place. These convection currents transfer heat from the horseshoe to the air via the water, which is the convection medium. If the water were surrounded by something solid or too viscous to flow, heat could only be transferred to the air via conduction, and it would take much longer. Convection plays a big role in determining global weather patterns.

Radiation The molecules of warm water cooling the horseshoe at the surface of Schmedrick's bucket bump into air molecules and transfer heat to the air via conduction. The water can also transfer energy to the air by emitting electromagnetic radiation. This is simply light, but usually it's light of a wavelength that is too long for us to see infrared. Bodies also continually absorb radiation, but when a body is warmer than its surroundings, it emits more than it absorbs. Night vision technology takes advan-tage of this fact by detecting infrared light in order to "see in the dark." Radiation can cool or warm objects even if they are surrounded by a vacuum. (Even a perfect Thermos bottle full of hot chocolate will eventually cool down.) When Schmed's bucket cools long enough, it will be in thermal equilibrium with the air, and the net radiation (emission - absorption) will be zero

Black Body A black body is an ideal absorber. It absorbs any radiation that is incident upon it (any light that hits it). It exists only in theory. All real-world objects interact this way with light. Only a black body would absorb all light, including wavelengths we can't see.

Sl Units for Thermal Conductivity H- A (T2-T k must have units that cancel out all the units on the right, leaving only the units for H. The units are: Wor equivalently, W m. K Since one kelvin is as big a change in temp as one degree Celsius, these units are equivalent. Note: k for thermal conductivity is not the same as the k in Hooke's Law in which it represents the spring constant!

Cold Tootsies Have you ever gotten out of bed in the wintertime and walked barefoot from a carpeted floor to a tile bathroom floor? The carpeting feels much warmer than the tile. But, assuming the house is in thermal equilibrium, the carpet and tile are at the same temp. So why does the tile feel colder? answer: The tile has a greater thermal conductivity constant than the carpeting does. That is, the carpet is a better insulator. So, even though their temps are the same, the tile draws body heat away from your tootsies more quickly than the carpet does. Thus, it feels as if the tile is colder.

R Value The R value of a material is its "thermal resistance" and refers to how good an insulator is. Here's how it's defined: As in previous equations: L = the thickness of the material k thermal conductivity of the material Note that the R value is inversely proportional to thermal conductivity, meaning good heat conductors have a low R value and are poor insulators. Also, the R value is directly proportional to the thickness of the material, meaning the thicker it is, the better it insulates. Thus, more insulation in the attic can save energy

Wind & Heat Loss A breeze can cool us off in the summer, and wind can make us feel colder in the winter. Why is this? answer. When we sweat the perspiration absorbs body heat, and when it evaporates, it takes this heat with it. This is called evaporative cooling. A steaming cup of hot chocolate cools in the same way. The reason a coat keeps us warm in the winter is because it traps air that is heated by our bodies. (Wearing layers is like having a triple pane window.) A thin layer of stagnant air also surrounds the outside walls of buildings and helps insulate them. Wind tends to blow this warm air away, along with its heat. The windier it is, the colder it feels to us, and the greater the heat loss from a building Trees around you home can save energy in two ways: blocking wind in the winter; and shielding your home from excess solar radiation in the summer

Laws of Thermodynamics Zeroth Law: If object A is in thermal equilibrium with object B, and if object B is in thermal equilibrium with object C, then objects A and C are also in equilibrium. This is sort of a "transitive property of heat." First Law: Energy is always conserved. It can change forms: kinetic, potential, internal etc., but the total energy is a constant. Another way to say it is that the change in thermal energy of a system is equal to the sum of the work done on it and the amount of heat energy transferred to it. Second Law: During any natural process the total amount of entropy in the universe always increases. Entropy can be defined informally as a measure of the randomness or disorder in a system. Heat flows naturally from a hot to cooler surroundings as a consequence of the second law.

Entropy (cont.) Macrostate # of Microstates Probability 1716 acrostate 3 (the group w/ 3 heads) is the most probable since it contains T H D H the most microstates (com- binations). Macrostate 2 has 6 microstates, so its probability is 6/16 3/ 8. This macrostate is the most random, or disordered, since there are so many ways 2 heads can come up in 4 flips. Entropy is a measure of disorder, and for this system it's at a max when in macrostate 2. Minimum entropy occurs when the coins are in macrostate 0 or 4, since there is a high degree of order in these states--only one microstate each. T T H T These are the least likely microstates to occur. D continued

Entropy (cont.) Suppose our coin system is in macrostate 4 (all heads). This represents maximum order, minimum entropy. Every so often one of the coins is chosen at random and flipped. With each flip there is a 50-50 chance that the macrostate will change. With time (after enough flips), it is doubtful that the system will still be in the minimum entropy state. It is much more likely to be in macrostate 2, the state with the most entropy. The 2nd Law states that during any process the universe moves toward more probably states--states with more entropy. It is possible to decrease the entropy of our coin system by physically turning all tails over so that there are all heads, but in doing this we must expend energy. This energy expenditure increases the entropy of our surroundings more than it decreases the entropy of the system. Thus the entropy of the universe is increased. continued on next slide

Entropy (cont.) In our coin example we only dealt with four coins. In real life even a quadrillion atoms or molecules might not be very much. (A single bacterium contains about 100 billion atoms.) How much more likely is it for a system to be in its highest entropy state than in its lowest? It depends on how big the system is: Ratio of Number of Coins 4 1 0 20 50 100 This means that if 100 coins were dumped on the floor it is about 100 billion billion billion times more likely for half the coins to come up heads than for all of them to be heads! Probabilities 2521 184,756 1 1014 1 10291 See next slide to see how these ratios are calculated

Entropy & Fluids Suppose a beaker of very hot water is poured into an aquarium of cool water. Conservation of energy would not be violated if all the hot water remained right at the spot where it was poured. But the 2nd Law demands that the thermal energy eventually become evenly distributed. The cool water has molecules moving at a wide range of speeds (red = fast, blue = slow). Since the water is cool, there are more blues than reds. The hot water poured in has mostly red. The aquarium has less disorder (entropy) when all the fast molecules are in one spot than when they are mixed in. With time a much more likely situation exists, with a much higher entropy continued time

Entropy & Fluids (cont.) Imagine how many different ways you could take 100 blue balls and paint 8 of them red. There are about 1.86 1011 ways to do this. Many, many more of those ways look like the picture on the right than on the left. The diffusion of perfume from an open bottle throughout a room is also a consequence of the 2nd Law. Unlike diffusion, though, the "hot water molecules don't necessarily have to move so that they are spread out evenly. Convection currents will allow some to move, but it is really the heat energy rather than the molecules themselves that must distribute itself equally throughout the aquarium.

Most Probable = Least Useful Kinetic energy, with many molecules moving in the same direction, represents an orgamzed for of gyChemcal potential enery, such as that coaned in ol is organized as well, since oil is comprised of long hydrocarbons with very specific arrangements of atoms. Gravitational potential energy is organized too, as in the card house All of these energies can be used to do useful work, such as lifting objects, generating electricity, etc. Thermal energy is always disordered unless there is a separation of temperatures. If hot water is separated from cold water, heat can flow and work can be done. An object or fluid with uniform temperature has uniformly distributed thermal energy and can't do any useful work. Unfortunately, this high entropy state is the most probable. Many scientists believe that the ultimate fate of the universe is a "heat death" in which the whole universe is at one uniform temp. This would represent maximum entropy. No life could exist, since life requires energy uptake and expenditure. This can't happen if the universe has only thermal energy.

Change in Entropy Equation Because most systems are many up of so many particles, calculating entropy via probabilities would be very difficult. Fortunately, we are normally concerned only with changes in entropy. If we have a system in which energy is not changing forms, the change in entropy is defined as: AS=AQ AS change in entropy Q = change in internal energy (heat flow) T absolute temperature The 2nd Law of Thermodynamics says that during any process: A S m ASsurroundings0

Second Law Consequences e Heat will not flow from a cold body to a hot body . "Reverse diffusion" is a no-no (such as smoke from a fire isolating itself in a small space) . An object or fluid of uniform temperature (no matter how hot) cannot do useful work. (There must be temperature difference so that there will be a heat flow, which can be used to do work.) . The various forms of energy tend to degrade over time to thermal energy. This represents useful, low probability forms of energy converting into an unusable, high probability form Without input of energy, bodies tend to reach thermal equilibrium. (We can maintain temperature differences via refrigerators or heating units, but this requires energy.) continued on next slide

Second Law Consequences (cont.) Any time we do something that decreases the entropy of a system the energy we expend in doing it increases the entropy of the surroundings even more. . A perpetual motion machine is impossible to make. A perpetual motion machine is a device that would absorb thermal energy from a hot body and do as much work as the energy it absorbed. (See pics on next slide.) During any process the entropy of the universe cannot decrease Expending energy to decrease the entropy of a system will lead to an increase in entropy for the surrounding by a greater amount.

Specific Heat Equation Q mCAT Q- thermal energy C specific heat m- mass AT change in temp Ex: The specific heat of silicon is 703 J/(kg. C). How much energy is needed to raise a 7 kg chunk of silicon 10 C? answer: Q-7kg . 703J kg.oC 10 . 10 C-49 2 10 J Note that the units do indeed work out to be energy units.

Latent Heat The word "latent" comes from a Latin word that means "to lie hidden." When a substance changes phases (liquid <solid or gas liquid) energy is transferred without a change in temperature. This "hidden energy" is called latent heat. For example, to turn water ice into liquid water, energy must be added to bring the water to its melting point, 0 C. This is not enough, however, since water can exist at 0 C in either the liquid or solid state. Additional energy is required to change 0 C ice into 0 C water. The energy increases the internal energy of the water but does not raise its temp. When frozen, water molecules are in a crystalline structure, and energy is needed to break this structure. The energy needed is called the latent heat of f sion. Additional energy is also needed to change water at 100 C to steam at 100 C, and this is called the latent heat of vaporization

Latent Heat Formula Q thermal energy m mass L = heat of fusion or vaporization L is the energy per unit mass needed to change the state of a substance from solid to liquid or from liquid to gas Ex: L (the latent heat of fusion) for gold is 6440 J/kg. Gold melts at 1063 C. 5 grams of solid gold at this temp will not become liquid until additional heat is added. The amount of heat needed is: (6440 J/kg) (0.005 kg) 32 J. The liquid gold will still be at 1063 C.

Po Calorimetry & Tigger SPOT Tigger greets Pooh in his usual enthusiastic manner. When he realizes that Pooh is storing a large vat of honey, Tigger bounces around the Enchanted Forest, and with one last, mighty bounce propels himself into the vat. Tigger's mass is m. His tail has a spring constant k and compresses a distance X. The honey's mass is M, and its specific heat is C. Assuming the honey gains all of Tigger's energy, how much does the honey's temperature rise? answer The elastic potential energy stored in Tigger's tail is converted to thermal energy in the honey: In real life AT would be slightly less since some of Tigger's original energy would have gone into heating the air and Tigger himself. Note that Tigger's mass and the height of his bounce matter not.

Thermal Expansion As a material heats up its atoms/molecules move or vibrate more vigorously, and the average separation between them increases. This results in small increases in lengths and volumes. Buildings, railroad tracks, bridges, and highways contain thermal expansion joints to prevent cracking and warping due to expansion. The amount of expan-sion depends on the original length/volumehe typcof maternal and the changen tempength is volume, T1 temp, is the coef-ficient of linear expansion, and is the coef. of volume expansion. When a solid of a single material expands, it does so proportionally in all directions. Since volume has 3 dimensions and length is only 1, Length expansion: Volume expansion: cold solid hot solid

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