Section 7 Laws Of Thermodynamics: Too Hot, Too Cold, Just .

Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just Rightobjective tool like a thermometer is required. The temperature andthe kinetic energy of the molecules change when the object touches amaterial of a higher or lower temperature.At the molecular level, the faster-moving, high kinetic-energy moleculescollide with the slow-moving, low kinetic-energy molecules, givingthem some of their energy. After many collisions, the average kineticenergy of the two original materials cannot be distinguished. The finaltemperature is that average kinetic energy.If object A and object B have the same temperature and object B andobject C have the same temperature, then object A and object C musthave the same temperature. Even though object A and object C maynever interact, you would know that their temperatures are the samebecause they are both compared to object B. This relation is referredto as the zeroth law of thermodynamics. Without this assumption, thestudy of thermal energy would be exceedingly difficult.Heat is a common word used in many different contexts. However,in physics, heat has a very specific meaning. Although you may oftensee the terms heat and thermal energy used to mean the same thing,scientists recognize a difference between the two terms.Thermal energy is the total energy of the particles that make up anobject. It is a form of energy that results from the motions of atomsand molecules, and it is associated with the temperature of the object.When the thermal energy of an object increases, there is an increase intemperature. You can think of thermal energy as the energy that an objectpossesses.Heat is the thermal energy that is transferred from one object toanother. Heat is a transfer of thermal energy from an object at a highertemperature to an object at a lower temperature.Thermal energy is a form of energy that results from the motions of atomsand molecules. The internal energy of a substance is the amount of energyin the random motions of atoms and molecules. (Random motion meansthat the atoms and molecules are moving in no specific pattern.) Thisincludes kinetic energy and potential energy of the interacting molecules.The amount of internal energy in an object has to do with the natureof the material, the mass of the material, and the temperature of thematerial. For example, 100 g of hot water has more energy than 100 gof cold water because of a difference in temperature. A swimming poolof 10,000 kg of cold water will have more energy than 1 kg of hot water,mainly because of a difference in mass. If the1 kg of hot water is pouredinto the swimming pool of 10,000 kg of cold water, the temperature of thepool water will rise a tiny amount. The temperature of the hot water willdrop considerably. Thermal energy is a measure of both the temperatureand the amount of matter.Physics Wordszeroth law ofthermodynamics: iftwo objects have thesame temperature asa third object, thenthe two objects mustalso have the sametemperature.heat: energytransferred fromone place toanother by virtueof a temperaturedifference.thermal energy: aform of energy thatresults from themotions of atoms andmolecules; the energyassociated with thetemperature of asubstance.thermodynamics:the study of therelationships betweenheat and other formsof energy and thetransformation of oneform into another.669Active PhysicsAP-2ND SE C6 v3.indd 6694/27/09 10:35:49 AM

Chapter 6 Electricity for EveryoneThe First Law of ThermodynamicsThermodynamics is the study of the relationships between thermalenergy and other forms of energy and the transformation of one forminto another. In this Investigate, you mixed hot and cold water andobserved how the final temperature of the mixture was related to theinitial temperatures of the hot and cold water. The change in thermalenergy of the hot and cold water were equal. The sum of the changes inthe thermal energy was equal to zero.The change in thermal energy of the water was dependent on the mass,the specific heat of water, and the change in temperature.ΔQ mcΔTWhen you mix cold milk with hot coffee, you expect the cold milk towarm a bit and the coffee to cool a bit. They will soon arrive at the sametemperature. This can be explained using the conservation of energy. Themilk gained some energy and the hot coffee lost some energy. It mightbe clearer if you look at some numbers. If the cold milk is at 5ºC and thehot coffee is at 90ºC, the final temperature of the milk-coffee mixturecould be 80ºC. In this case, the temperature of the milk rose 75ºC and thetemperature of the coffee fell 10ºC. Energy was conserved. If you knewthe mass of the coffee and the milk, you could compute the gain and lossof the energy by each substance using the relation Q mcΔT . The changein energy of both the milk and the coffee would be the same.This situation is quite common. If you put a cup of hot coffee in a coldmetal cup, there would be a similar effect. The coffee could cool from90ºC to 80ºC and the metal could warm from 5ºC to 80ºC. If you knewthe masses of the metal and the coffee and the specific heat of themetal, you could again compute the gain and loss of the energy with therelation Q mcΔT . Again, the change in energy would be the same forthe metal and for the coffee.Physics Wordsfirst law ofthermodynamics: thethermal energy addedto a system is equal tothe change in internalenergy of the systemplus the work doneby the system on itssurroundings.The conservation of energy with respect to hot and cold objects isreferred to as the first law of thermodynamics. In the situations you havestudied, the hot and cold materials did not interact with other materials.The hot and cold materials did not get heated from the outside nor didthey use any of their thermal energy to do work by moving something.The first law of thermodynamics can also explain what happens if one ofthese two situations did occur.Imagine a gas that is enclosed in acontainer with a movable top (a piston).Initially, the gas has a certain amount ofthermal energy. The kinetic energy of themolecules that keep colliding with thepiston keep it up. If an external flamewere to heat the gas, the piston wouldmove up. The gas did work on the pistonby lifting it.670Active PhysicsAP-2ND SE C6 v3.indd 6704/27/09 10:35:49 AM

Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just RightThe conservation of energy would state that ΔQ ΔU WThe thermal energy ( ΔQ ) added is equal to the change in internal energy( ΔU ) of the gas plus work (W ) done lifting the piston. This is anotherway of stating the first law of thermodynamics.The Second Law of ThermodynamicsWhen hot coffee is poured in a cold metal cup,it never happens that the metal gets even colderand the coffee gets even hotter. It never happensthat the coffee heats up from 90ºC to 92ºC andthe metal cools from 5ºC to 1ºC. In principle, theconservation of energy would be satisfied if thecold metal lost thermal energy and the coffeegained an equal amount of thermal energyso that no energy was created or destroyed.However, this never happens. It also neverhappens that if you leave a can of warm cola onthe kitchen table that the cola gets colder andthe room gets warmer.If something never happens, you must assume thatnature has placed a restriction on it. In this case,the restriction is called entropy. It informs you thatthe two materials in contact will reach a commonequilibrium temperature. The transfer of heat canonly take place in one direction — from hot tocold. Temperature tells you which way the thermalenergy is transferred. A cooler metal will heat up(gain heat) when placed in contact with the hotcoffee, but the cooler metal will never becomecooler (lose heat) when placed in contact with thehot coffee.Physics Wordsentropy: athermodynamicproperty of asubstance associatedwith the degreeof disorder in thesubstance; a substanceis more ordered as asolid than a liquid,and a liquid is moreordered than a gas.This irreversibility of heat flow helps to distinguish the past from thefuture. If you watch a movie of a pendulum moving back and forth,you may not be able to tell whether the film is being played forward orbackward. If you watch someone break an egg and fry it, the film wouldlook quite silly when played backward. It doesn’t make sense that theegg could get un-fried and then return to its shell. Similarly, water in aglass in a warm room will never suddenly freeze into ice cubes and makethe room warmer.The irreversibility of heat flow is related to the entropy of the substancesand is related to the order and disorder of the system. When hot andcold water are mixed, entropy (disorder) increases. When a solid turnsto liquid or a liquid turns to gas, entropy (disorder) increases as well. Amathematical understanding of entropy requires a careful look at thepossible distributions of energies of the molecules and can bedescribed using statistical physics.671Active PhysicsAP-2ND SE C6 v3.indd 6714/27/09 10:35:50 AM

Chapter 6 Electricity for EveryoneYou can get a sense of order and disorder and entropy by considering twogases reaching an equilibrium temperature. On one side of a container,you may have 50 fast-moving molecules. The other side of the containerhas 10 slow-moving molecules. If the two sides came into contact, youwould expect that eventually the fast-moving molecules and the slowmoving molecules would collide often enough that the fast-movingmolecules would slow down and the slow-moving molecules would speedup. This is an example of entropy increasing or disorder increasing.Physics Wordssecond law ofthermodynamics:thermal energy istransferred fromhot objects to coldobjects and nevergoes from cold to hotspontaneously.Imagine the opposite occurring. If you had a container with 60 movingmolecules, could you imagine all the fast-moving molecules speedingup, the slow-moving molecules slowing down and the fast moleculesall going to the left side of the container and the slow molecules allgoing to the right side of the container? This would be an example ofentropy decreasing or disorder decreasing. It is possible, but it is very,very improbable. The only way you would expect to see the entropydecreasing is if someone deliberately did this and expended energysorting the molecules.Checking Up1. How is temperaturedefined in terms ofmolecular action?2. When cold milkis added to hotcoffee, the milkwarms up and thecoffee cools down.What can be saidabout the energyof the milk andthe energy ofthe coffee whenthis happens?3. The amount ofthermal energythat is gained orlost by an objectdepends uponwhat three things?4. In a process that isnot reversible in aclosed system, whatalways happensto the entropyof the system?The second law of thermodynamics can be stated in a numberof different ways: In irreversible processes, entropy or disorder always increases. Time is irreversible. Thermal energy is transferred from hot objects to cold objectsand never goes from cold to hot spontaneously.672Active PhysicsAP-2ND SE C6 v3.indd 6724/27/09 10:35:50 AM

Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just RightActive Physics Math Depth ConceptsEntropyImagine that there are three spheres in a boxthat has two sides. Each sphere is a differentcolor—red, blue, purple. The possibleconfigurations of the box are as follows:Left sideof the boxR, B, PR, BR, PB, PRBPRight sideof the box ExplorationPlus2. Using your calculations, explain whyit appears that entropy or disorderwill increase as the number ofparticles increases. In other words, ifyou were to start with all the particlesin a box on one side, explain why youwould expect to never see them onone side again.In a one-liter bottle, there are over 1020molecules of air. Can you imagine theprobability that all the molecules would bein the bottom half of the bottle?PBRB, PR, PR, BR, B, PThe Heat Engine and the SecondLaw of ThermodynamicsOnce again, imagine a gas that is enclosedin a container with a movable top (apiston). Initially, the gas has a certainamount of thermal energy. The kineticenergy of the molecules keep collidingwith the piston and keep it up. If anexternal flame were to heat the gas, thepiston would move up. The gas did workon the piston by lifting it.Of the eight possible configurations,only one has all the particles on theleft side of the box. That makes thisconfiguration less likely than others wherethe particles are on both sides of the box.The configuration where all particles areon the left side of the box can be said tohave low entropy and low disorder. Ifall the particles were to start on the leftside of the box and were free to moveabout, you would expect at some latertime to observe the particles more evenlydistributed. There are six configurationswhere the particles are on both sides ofthe box. These represent higher entropyor higher disorder.1. Repeat this example and find theprobability for all the particles in thebox to be on one side if there werefour, five, or ten particles in the box.For ten particles in the box, you willprobably want to find a mathematicalpattern rather than writing out allpossible configurations.If the gas were then cooled by placingit in touch with a cold object, the gasmolecules would lose kinetic energy andthe piston would move down.673Active PhysicsAP-2ND SE C6 v3.indd 6734/27/09 10:35:51 AM

Chapter 6 Electricity for EveryoneThis is the basis of a simple heat engine:Heat the gas and move the piston up; coolthe gas and move the piston down. If youkeep repeating this, the piston moves upand down over and over and can turn thewheels of a car.It would be great if this engine could be100% efficient. That would mean that allthe heat would get converted to mechanicalenergy. The laws of nature do not allow this100% efficiency. This is another statementof the second law of thermodynamics.Sample ProblemA heat engine consists of a quantity ofgas in an enclosed cylinder with a masslocated on top as shown in the diagrambelow. The mass can move freely up anddown as the gas expands.a) Strategy:Since the gas and the flame represent aclosed system, the energy added by theflame must go to either increasing theinternal energy of the gas, or towardwork done by the gas.Given:ΔQ 2000 JΔU 1900 JSolution:Using the first law of thermodynamics:ΔQ ΔU WSolving for WW ΔQ ΔU 2000 J 1900 J 100 Jb) Strategy:Work done equals force distance,where the force the gas expands againstis the weight of the piston that holds it inthe cylinder.Given:W 100 JF 500 NSolution:Using the equation for work:W F dSolving for da) If 2000 J of heat are added to thecylinder and the internal energy ofthe gas increases by 1900 J, causingthe gas to expand, how much workis done by the gas as it expands andmoves the piston?b) How high will the piston rise?WF100 J 0.2 m500 NIf heat were now extracted from thecylinder, the gas would typically cool andthe piston would fall as the gas contracts.d 674Active PhysicsAP-2ND SE C6 v3.indd 6744/27/09 10:35:51 AM

Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just RightWhat Do You Think Now?As you add cold milk to hot coffee, you expect that the milk will get a bit warmer and thecoffee will get a bit colder. What determines the final temperature of the coffee and milk?Now that you have completed this section, how would you answer this question now?PhysicsEssential QuestionsWhat does it mean?How does energy conservation help predict the final temperature when hotand cold water are mixed together?How do you know?What measurements did you have to record to show that energy was conservedwhen hot water was placed in cool water?Why do you believe?Connects with Other Physics ContentThermodynamicsFits with Big Ideas in ScienceConservation lawsMeets Physics RequirementsExperimental evidence is consistent withmodels and theoriesConservation of energy is a bedrock principle of science. Conservationof energy is considered one of the greatest insights into how natureworks. What do people mean when they ask you to conserve energywhen you know that energy is always conserved?Why should you care?Electricity can be used to heat water. People often heat an entire pot of waterto make one cup of tea. This is a very wasteful use of resources. Write a note topeople to convince them to only heat the water they need. Emphasize the amountof energy required to heat water.675Active PhysicsAP-2ND SE C6 v3.indd 6754/27/09 10:35:51 AM

Chapter 6 Electricity for EveryoneReflecting on the Section and the ChallengeHeating water for purification or cooking food is a matter of survival. You maydecide to use your limited amount of electrical energy to perform these importanttasks. It will be crucial to calculate the energy required to change the temperatureof water or foods. You know that a cold drink will warm up if it sits on the tableand that a hot drink will cool down if it sits on the same table. All objects in thedwelling will reach the same final temperature—the equilibrium temperature.You can now calculate the energy changes when cold objects and warm objectsare put in contact.Physics to Go1. A hot cup of coffee at 90 C is mixed with an equal amount of milk at 80 C.What would be the final temperature if you assume that coffee and milk haveidentical specific heats?2. Explain why heating up a whole pot of water when you only need enough forone cup of tea is wasteful of time and wasteful of energy consumption.3. A container of water can be heated with the addition of hot water or theaddition of a piece of hot metal. If the mass of the water is equal to themass of the metal, which material will have the greatest effect on the watertemperature? Explain your answer.4. Suppose 200 g of water at 50 C is mixed with 200 g of water at 30 C.a) What will be the final temperature?b) Calculate the energy gained by the cold water.c) Calculate the energy lost by the hot water.5. Suppose 200 g of water at 50 C is placed in contact with 200 g of ironat 30 C. The final temperature is 48 C.a) Calculate the energy gained by the iron. The specific heat (c) of ironis 0.45 J/g C.b) Calculate the energy lost by the hot water.c) If the final temperature could have been measured more accurately, wouldyou expect that it would have been a bit more or less than 48 C? Why?6. Suppose 100 g of water at 50 C is placed in contact with 200 g of iron at30 C. The final temperature is 46.5 C.a) Calculate the energy gained by the iron. The specific heat of iron is 0.45 J/g C.b) Calculate the energy lost by the hot water.c) If the final temperature could have been measured more accurately, wouldyou expect that it would have been a bit more or less than 46.5 C? Why?676Active PhysicsAP-2ND SE C6 v3.indd 6764/27/09 10:35:52 AM

Section 7 Laws of Thermodynamics: Too Hot, Too Cold, Just Right7. Suppose 300 g of water at 50 C must be cooled to 40 C by adding cold water.The temperature of the cold water is 10 C. How much of the cold water mustbe added to the hot water to bring the temperature down to 40 C?8. 100 g of water at 80 C is placed in contact with 100 g of water at 40 C.a) Show tha

When 100.0 g of hot water at 80.0 C is mixed with 60.0 g of cold water at 20.0 C, the final temperature is 57.5 C. Show that energy was conserved. Strategy: Heat is a form of energy. The law of conservation of energy tells you that the thermal energy (heat) lost by the hot water is going to equal the thermal energy (heat) gained by the cold .