Calorimetry

[00:00:01][Applause] [Music] so what happens when you put a paper cup of above a Bunsen burner okay an empty cup well no surprise you reach the combustion point of paper okay Fahrenheit 451 pretty quickly let's see what happens when you put a cup of water over that same Bunsen burner and you will notice that you don't get the same result hmm what is the difference in what you observe obviously that paper cup is not reaching the Fahrenheit 451 temperature okay why not what is the effect of the water in that cup there you see it boiling some strange colored water and must say so before we can understand why a paper cup of water held above a 600 plus degree Bunsen burner flame doesn't combust when we know that paper has a combustion point of about 230 degrees Celsius okay before we can understand that we need to formally introduce the concept of heat now from our last lecture we now know what temperature measures right okay it's a measure of the average kinetic energy of the particles that make up an object okay but what about heat we must be a bit careful here because while we're all familiar with the word heat okay we need to make sure that we distinguish heat from a related concept called internal energy sometimes referred to as thermal energy so we're going to take a trip back in time to visit an old outdated no longer believed in theory okay of heat and if you ask you know why would we do this well very often it becomes difficult to learn new physics because we have very defined K theories based upon our own observations and experiences interacting in the world and so some of these ideas in the caloric theory are certainly consistent with what we observed in the everyday world okay and there's obviously a reason why they came up with it I mean it was based upon common experience and observations that a lot of people had so it's it's worth looking at you know some of these beliefs that many listen may have old which are no longer considered scientifically valid so up until about a hundred and fifty years ago okay it was the caloric theory that was used to explain the concept of heat and the theory went something like this okay he was thought to be an invisible fluid called caloric and the idea being that an object possessed a certain amount of caloric and when an object had caloric added to it okay had heat out to it well then its temperature would increase when an object lost caloric for whatever reason okay the temperature of the object would decrease so the temperature of an object okay was directly related to the amount of caloric that the object possessed and it was thought that when an object is subdivided okay like in the case of cutting for example okay the caloric is being released and this could explain the decrease in temperature of the object itself but also nice to explain the increase in temperature witnessed in the surroundings so even today we still use the term heat flow as if okay heat was some sort of fluid this so often happens in science and observation or discovery is made that is inconsistent with the current model okay the current theory this is exactly what happened the caloric theory in the mid-1800s okay a okay followed by the name of Benjamin Thompson okay more commonly known to society as count Rumford made some observations in the process of boring out canons now when you think about how canons were made back then large cylinders of solid iron were bored out using drills I mean drill bits very often turned by teams of horses and in the process of boring out the cat these solid cylinders of iron water was used to cool the cutting instruments okay um but eventually these cutting instruments would get too dull to actually cut the metal okay and what can't look for notice is that even when the instruments got so dull they could no longer subdivide the metal okay the temperature the water used in the cooling process still continued to increase and he noticed that this process could take place indefinitely meaning there was really no limit to how much water could get heated well think about what we said on the previous slide about the caloric theory that if caloric is being released by an object there should be a finite amount of caloric that is being released eventually okay the object should run out of caloric and secondly that only if an object was actually subdivided would it actually be able to release caloric so here you know we can state these questions raised by these observations that count run fur that contradicted the caloric theory first of all how could caloric be released when the dhol instruments could no longer subdivide matter okay and secondly if caloric was a fluid it should exist in a finite amount in eventually a sample of matter should run out of it okay so how could he be generated indefinitely okay during the cannon boring process so you can see how these problems okay like very often happens in science okay leads to a new theory okay which can explain them so our modern definition or modern interpretation of heat which is based on kinetic molecular theory goes something like this okay heat and we'll use a symbol Q to represent he he is a transfer of energy okay from an object at a higher temperature to an object at a lower temperature k caused or due to a temperature difference between these two objects so it's really important to note here that heat is not energy okay but is rather a transfer of energy so in the same way that work is not energy but is rather a transfer of energy due to mechanical means or forces the same can be said about heat heat is not energy but it's rather a transfer of energy that happens for a different reason than work okay it's the transfer of energy that happens because of a temperature difference okay this is something we'll talk in greater detail about we talk about the first law of thermodynamics so when it comes to units to measure heat we have the problem of history okay as we do very often with other physical quantities and that is that although the definition of heat has evolved throughout the ages okay and we see that we no longer believe in the caloric theory today but the kinetic molecular theory gives us an interpretation of heat okay although the theories have evolved were still stuck we still okay hold steadfast to some of these old units that were introduced a long time ago so we have to at least be familiar with them now the old SI unit okay was the calorie and this is as you can see was part of the caloric theory so and we still see this unit very often so you do need to be familiar with it the calorie symbolized Cael okay by definition is the amount of heat that is required to raise the temperature of one gram of water by one degree Celsius technically from 14 and 1/2 degrees Celsius to 15 1/2 degree Celsius now why does 10 why this definition is used to define the calories can become a lot clearer when we talk about the idea of specific heat capacity it related unit the kilo calorie or kcal or to make things really confusing just a calorie with a capital C okay is a thousand calories it's important to note here that when you talk about food calories when you look at the back of a food package and they you know tell you how many calories item house for a typical you know let's say 20 400 calorie a day diet trust me you would die very quickly if you were only eating or ingesting 2,400 calories a day you're really ingesting okay typical diet of gave 2,400 capital calories or cake house so we're really ingesting more like okay two million four hundred thousand small calories a day so I have no idea why that's the case it is confusing but make a mental note of it okay food calories really eight kilocalories of course our modern understand you 'not to measure heat if if heat is a transfer of energy then you would expect it to have the other energy units so of course we know that joules is our SI unit that we use to measure energy and okay you you know a tool is okay kilogram meter squared per second square the British unit still come across if you're gonna buy a water heater for example you might see okay a rating and BTUs or British thermal units and the British thermal unit is the amount of heat required to raise the temperature of one pound of water okay from by one degree Fahrenheit from 63 degrees Fahrenheit to 64 degrees Fahrenheit so you see here that our definition of the BTU looks pretty similar to the concept of the calorie and we'll see why as I said once we understand the meaning of specific heat capacity okay that will give us an understanding for how much heat gets transferred to or from an object now James Prescott Joule okay a bust who you see on your screen here okay and the scientists that we all know and love um he while on his honeymoon okay had always wanted to show that when water fell through a certain distance 778 feet to be exact that the temperature of the water would rise by one degree Fahrenheit okay for such a fall height so James Joule had this opportunity on his honeymoon he married a lady by the name of Amelia Grimes and on this honeymoon he visited a waterfall and conducted a series of experiments he measured the temperature of the water at the top of the Falls then measured the temperature again at the bottom of the Falls because he suspected that the work done came by the falling water would increase its temperature and that is exactly what he found out okay so what would a truly romantic thing to do on your honeymoon okay be sure to take good notes everybody okay especially for those of you who were not yet married um but James Joule does get credited with discovering this relationship okay between work and heat and this is what we call the mechanical equivalent of heat and he discovered this exact relationship through his famous paddle wheel experiment okay that looks something like this you can see here we have a chamber with a paddle wheel that chambers filled with water and these weights can be cranked up to a certain height okay by turning the crank and so doing a certain amount of work would be done by the paddle wheel on the water and you can see the thermometer there that amount of work could okay what would increase the temperature the water which could be measured certainly when those weights then fall their loss of gravitational potential energy would get converted into the thermal energy they get transfer to the water in the form of heat and again raises temperature so with enough of these turns you know tool is able to very accurately figure out what that correlation was between okay the energy added to the water and the change in temperature of the water okay the the amount of heat that was transferred on and this is this is what we call the mechanical equivalent of heat so you will discover that doing a given amount of work on an object always produced a certain amount of heat what is that amount of heat so what we call the mechanical equivalent of heat and it turns out that okay four point one eight six joules of work is equivalent to one calorie of heat so this mechanical equivalent of heat can really be thought of as nothing more than a conversion factor okay between work and heat and we'll take a look at a problem okay one that's you might find interesting okay that will make use of this of equivalent of heat so it turns out that lovemaking requires between 500 and 1500 kilojoules of work depending on fervor course so we're asked to find how many food calories would a very fervent three rounds per week person lose in a year if no additional food were eaten to match his or her sexual appetite so treating this is a converting units problem okay we will start here notice here that we have okay this is a very fervid individual we're talking about here okay obviously someone much younger than myself so we'll go with the 1500 kilojoules cape around and times three rounds per week okay we'll give us how many kilojoules per week and if we want to convert this since we're asked to find out okay how much how many food colors would be lost in entire year will convert weeks into years okay by x 52 weeks to the year and now we get to use our mechanical equivalent of heat okay so if 4.18 joules is equivalent to one small calorie we can say the four point one eight kilojoules is equivalent to one kilo calorie or food calorie so this turns out to be 56,000 kcals per year so the more interesting question that we all want to know I'm sure is you know how much how much weight would such a person lose in a year okay given that the energy content of one gram of fat is 9.6 kilocalories so okay given this form of exercise how much weight could be lost in a year assuming of course that you don't you know how that goes if you get hungry you're gonna eat more to make up for that's one of the problems with you know being using activity being very active to actually lose weight is that you and you tend to be you know hungry or when you're you're getting more exercise but assuming that you know we're just gonna do the calculation here so again a conversion factor so we'll take the 56,000 kcals per year okay we will turn that into a a mass in grams noting that one gram of fat is equivalent to 9.6 kcal so this is this is 1,500 grams or 5.8 kilograms per year when you convert that to pounds about 13 pounds per year so like I said some sounds like a lot okay and you know assuming that that food was not additional food was not eaten okay - you know replace those calories burned okay then about 13 pounds per year could be lost okay given this activity so we say that heat is a transfer of energy okay from one object to another due to a temperature difference but how do we actually measure the energy of the system itself okay well they related quantity okay but distinctly different is what we call internal energy and we will use the symbolism capital e with the subscript int to represent the internal energy of a system so what do we mean by the internal energy of the system we're talking about the sum total that is all forms of microscopic energy that means the total microscopic kinetic energy okay due to all forms of kinetic energy as well as all forms of microscopic potential energy associated with that system now you'll notice here this condition that says when viewed from the reference frame at rest with respect to the center of mass of the system well think about this you know that when we talked about the kinetic energy of an object okay it depends upon the speed of the object will you know that the speed of an object okay it's gonna be dependent upon the reference frame from which it is measured in one reference frame an object might not have speed okay but another reference frame it would so clearly the reference frame will affect okay your measure of the kinetic energy of the object so that's why we add in this condition okay when viewed from a reference frame at rest with respect to the center of mass of the system we'll talk more about that in the next slide so when we think about the microscopic energy we're talking about the energy associated with the particles that make up the object now I use the word particles very generally the particle could represent an atom if your system could consist of atoms let's say noble gas atoms okay we're you know these atoms will not combine with other atoms okay or your system could consist of molecules where you do have atoms that combine with other atoms to form molecules or your system could consist even of ions so we use the word particle very loosely so what are these specific forms of microscopic energy okay whether kinetic okay or potential let's take a look so when we talk about the microscopic energy of the system we could be referred to the vibrational kinetic energy of the system now you know that solids okay which do not have a whole lot of emotional freedom most of their kinetic energy their emotional energies in the form of vibrational kinetic energy is this simulation shows they they solids do not have a lot of rotational and translational freedom okay but if we talk about liquids okay liquids the particles have the ability not only to vibrate okay with respect to each other but also to rotate around each other and that's what gives liquids this ability to flow so we have to look at the rotational kinetic energy as well when we talk about gases we know that gases have the ability to do gas particles can completely move apart from each other they can move from one side of the container to the other this is translational kinetic energy so we have to look at that form of kinetic energy as well when it comes to potential energy okay we have to look at the potential energy due to the entry particle bonds as well as the inter particle bonds when I talk about intra particle bonds these are bonds okay within a given particle so this would only apply to cases where you have let's say molecules that consists of two or more atoms and you can see here that this is a given particle on your screen but which consists of a collection of okay three different atoms and you can see here if this was a water molecule that those pipe there's a bond between each hydrogen atom and the oxygen atom and there is a bond energy there's potential energy associated within that bond that is an intra which means okay between atoms here an intra particle bond okay not to be confused with an inter particle bond this would be bonds between particles so what you're seeing illustrated here are two particles and if I can get my laser pointer here you'll see that these two particles are being joined okay there is a bond between these two particles right here which possesses potential energy so that is an inter particle bond so in this slide we'll take a closer look at the difference between the microscopic energy of the system and the microscopic energy of the system so we'll consider a simple system here if I was giving this lecture face to face I would do this in front of you but okay here we'll just use a picture consider we have two tennis balls identical in all respects except that one is is on the table the other is on the floor okay you see that you know really the only difference okay between these two balls is that one exists at a greater height okay relative to the center of the earth so which of these tennis balls has the greater internal energy okay well clearly you see that the one on the table has a greater maker scopic energy right because it has more gravitational potential energy than the ball on the floor okay on but that's not what we're interested in when we're interested in microscopic forms of energy okay assuming that the particles within each tennis ball have the same amount of microscopic kinetic energy they're moving it okay the same speeds they have you know the same level of vibrational rotational and translational kinetic energy on as well as okay both forms of intra particle and inter particle potential energies so here um we can say that both of these tennis balls have the same microscopic energy although they clearly have different amounts of maker scopic energy because the ball on the table has a greater maker scopic potential energy okay let's assume now that one ball rolls off the table here okay um how does its internal energy compared to the ball on the ground while it's falling well once again okay we can say that the ball that is falling has a greater maker scopic kinetic energy all of those particles in addition to their microscopic random vibrational rotational translational motions within the ball okay in addition to that now they all those particles are moving downwards with the kinetic energy the makers got the kinetic energy of the ball but you see that that is a maker scopic form of energy okay and that is why we add this condition when viewed from a reference frame at rest relative to the center of masses so you see that even while that tennis ball is falling okay and all those particles have a maker scopic kinetic energy would measure from the reference frame okay of the floor okay when measured from a reference frame on the center of mass of the moving ball okay now you can see that the moving ball those particles have the same kinetic energy when measured from that reference frame as the ball on the ground okay so although the following ball has a greater amount of makers got the kinetic energy it's a microscopic kinetic energy will be the same as the one on the ground assuming that you know we neglect the air friction in the particle okay making that assumption and then you can see the difference between maker scopic kinetic energy and forms of microscopic kinetic energy so now that we've formally defined the concept of internal energy in this video as well as the concept of heat let's make a comparison between these two quantities as well as the concept of temperature which we defined according to kinetic molecular theory in our previous lecture so just in one slide let's just kind of review the differences between these three quantities in their definition so when we talk about the internal energy of an object of a system okay we're talking about the total microscopic energy of all part of the particles in the object and okay we just said there's many forms of microscopic energy both microscopic kinetic energy in the form of vibrational rotational and translational kinetic energy as well as the two forms of microscopic potential energy temperature you recall is the measure of the average translational kinetic energy of the individual particles in an object so this is a little bit of a restriction here so technically when we talk temperature we're talking about okay the translational kinetic energy of the particles only okay we're ignoring the rotational and vibrational forms of kinetic energy when we talk about heat we're talking about not energy itself but the transfer of energy between objects due to a temperature difference all right so in this slide we will take a look at a specific example that will illustrate the differences between these three related yet distinctly different quantities that is internal energy versus he versus temperature in order to do so we will take a look at two systems and take a look at each of these quantities okay in each of these two systems so these two systems the mug of hot coffee versus the backyard swimming pool so if I were to ask which of these two objects the hot cup of coffee or where the swimming pool has the greater or higher temperature and why well certainly you don't need to take a course in physics to know which of these objects is at the high temperature can you have enough life experience to tell you that okay it's gonna be the hot cup of coffee but to answer why you would need to know the meaning of temperature we would say that on average the particles in the coffee really the molecules of water in the coffee have a greater kinetic energy on average than those water molecules in the swimming pool and therefore the hot cup of coffee is at a higher temperature but were then to ask you which of these two objects has the greater internal energy and why okay whereas temperature is a measure of the average kinetic energy of the particles that make up an object internal energy is a measure of the total microscopic energy of the particles that make an object so here even though the particles of water in the swim pool are not moving quite as fast on average as those in the hot cup of coffee okay there are so many more particles in the swimming pool that even though they are moving slower okay when you look at the sum total the total energy of all the particles okay the swimming pool is gonna have a lot more internal energy than the cup of coffee and finally if we were to say which of these objects which of these systems would heat your finger more and why well again you from your your life experience you know that you can stick your finger in a swimming pool and it's not gonna okay each finger much okay but do it in the hot cup of coffee and it's certainly gonna heat your finger a lot more why well because we talked about heat we're not talking about a transfer of energy and it turns out that the object that is at the higher temperature okay will be able to transfer more energy to your finger okay before thermal equilibrium is reached now this next concept will introduce in this unit is a concept that we call specific heat capacity and it turns out that specific heat capacity is one of three factors that will affect temperature change when heat is being added or removed from an object so rather than simply tell you what these factors are i I would like to play a guessing game and see if you can use your life experience to make some predictions about what these factors are so here's the the puzzle or the guessing game the challenge that I proposed to you I am thinking of some unknown object sounds sort of like 20 questions right now suppose you add heat to this object can you think of three properties that is three factors that will affect how much the temperature of this object will change and then once you've identified these three factors Howry to these factors related to the temperature change and in other words is there a direct relationship or an inverse relationship so you may want to pause the presentation here and think about these see if you can come up with any of these these three properties alright so let's see how good you were at actually solving this puzzle so of these three factors the first factor that we'll talk about is really the size of the object now there's lots of ways to measure size but one of the ways to do this is in terms of the mass of the object and hopefully you would agree that if you're going to add heat to an object that the amount that objects temperature will change will depend upon its size imagine trying to heat a sample of water on your stove certainly you know that if you want to heat a small amount of room-temperature water up to boiling on that its temperature will change okay much more for a given amount of heat then if you're trying to heat up a large amount of water so in other words adding a certain amount of heat to a small amount of water will change its temperature much more than adding the same amount of heat to a large volume of water so that tells us then that there is an inverse relationship between the size of the object and its temperature change okay that small objects will experience much greater temperature changes now a second factor and this one may be so obvious that you overlooked it is the amount of heat added obviously if you add a small amount of heat to an object its temperature will not change nearly as much as if you add a large amount of pee this tells us that there's a direct relationship between the amount of heat added and the temperature change adding more heat causes bigger changes in temperature now this third and final factor or property is what we call specific heat capacity and we'll talk in greater detail about this in the next slide but for now realize that the specific heat capacity of a substance is dependent upon what the substance is made out of upon the type of substance and a good way to think about specific heat capacity is to think about it is a measure of thermal inertia and we know that inertia is a measure of a resistance to change and thermal inertia we can think of as a resistance to changes in temperature so if a substance has a high specific heat capacity like water let's say that means that it has a lot of thermal inertia that it has a great resistance to having its temperature changed a substance with a much smaller specific heat capacity will change its temperature much more readily and because of this definition it turns out that there's an inverse relationship between pacific heat capacity and temperature change that is substances with high specific heat capacities don't change their temperature very much when heat is added so in this slide let's summarize the results from this very fun game we played on the previous slide and in conclusion we can say these three factors okay that effect the temperature change of an object okay we can express it like this we can say that okay the temperature change of the object is directly proportional amount of heat a bit okay add more heat get a bigger temperature change it is inversely proportional to mass of the odd okay the greater the mass of the object the smaller the temperature change and the way we define this quantity we call specific heat capacity we can say there's also an inverse relationship okay that an object with a large specific heat capacity would experience a smaller temperature change okay for a given amount of heat added we cannot express ok these relationships and what I call the sing-along version of this relationship let's get our singers here we can say that Q is exactly equal to MC delta T has a nice ring to it doesn't it and the way we define this quantity called specific heat capacity it really becomes our proportionality constant okay in this relationship and it turns out like we said in the prior slide that the specific heat capacity of substances substance dependent okay it depends on the actual type of substance that we're talking about all right so what exactly do we mean by the specific heat capacity of a substance let's formally define it the specific heat capacity symbolized with little C is the amount of energy required to raise a unit mass of a substance okay we usually use either a gram or a kilogram by one degree Celsius okay so how much energy is required to raise a unit mass of the substance to raise one gram of a substance by one degree Celsius and we said that different substances okay require more energy okay to bring about a given temperature change so we can think of the specific heat capacity of substances really being a measure of the thermal inertia of a substance remember that if we think of inertia as a resistance to a change okay the way we talked about inertia when we talked about mechanics we said it was a resistance to a change in the state of motion that mass was a measure of inertia get more mass an object had or it resisted having its state of motion changed in the same way here we can say that the higher the specific heat capacity of a given substance the more resistance it has to having its temperature changed and just like you know in the case of the inertia we talked about a mechanic's you can change the state of motion of an object but not with greater inertia requires a greater force to do so in the same way here we can say that a substance with a higher specific heat capacity would require more heat added to it okay more energy transfer to it in order to change its temperature by a given amount like one degree Celsius so I think this is a good way to think about it think of heat specific heat capacities measure of thermal insensitivity okay or thermal inertia ah when it comes to units okay when we take our Q equals MC delta T sing-song equation here and solve it for specific heat capacity we see that K Q heat is going to be measured in joules okay mass either in grams or kilograms and temperature in degrees Celsius so we can our most common units for specific heat capacity or joules per gram degree Celsius or joules per kilogram degree Celsius so in this slide we'll take a look at the specific heat capacities of some common substances at 25 degrees Celsius and what you should note here okay if you take a look at some of these values is that water over here has a very high number compared to let's say these metals gold and let down here at the bottom and if we take a look at the meaning okay what's the significance of that well this would tell us that water for water it takes 4186 joules to raise one gram of water by one degree Celsius whereas when we look at gold it takes only a hundred and twenty nine jewels okay to raise the temperature of one kilogram of gold by one degree Celsius so you can see here that water is kind of special okay water is very thermally insensitive it has a high thermal inertia it takes a lot of energy added to be able to raise its temperature okay by one degree Celsius and we put that on the slide here water has a very high specific heat capacity and we can say that in general metals can have low case specific heat capacities this gives water some very unique properties okay and important properties it we'll take a look at in the next slide alright so in this slide we will take a look at some conceptual examples okay involving specific heat capacity in particular taking a look at the particularly high specific heat capacity of water so the first example we asked why is the climb is so moderate for coastal regions of California why is it that California real estate is so much more expensive in the coastal climates than it is here inland in the Central Valley well believe it or not it all has to do with specific heat capacity of water the high specific heat capacity of water allows the ocean to absorb a great deal of thermal energy from the atmosphere care from the Sun in the summertime without raising its temperature too much so think about it the Sun beats down on the ocean ocean absorbs of that energy and it doesn't raise this temperature very much that keeps the surrounding atmosphere at around quite cool when that same Sun beats down on the inland region of the Central Valley okay unlike water the temperature of the land raises quite a bit and since that's in contact with the atmosphere raises the air temperature a lot too so that's what happens in the summertime but think about it that ocean that huge body of water has behaved as this huge storehouse is huge reservoir of energy absorbing the energy from the Sun in the summer but then in the wintertime when the air temperature K drops below the ocean temperature now all that stored energy can get released back into the environment keeping the air temperatures much warmer than they would normally be okay here in Modesto in the Central Valley we don't have that advantage okay the land has not stored nearly as much energy okay during the summertime okay to be able to release it in the winter time we keep the air temperature warmer okay so high specific heat capacity of water has everything to do with real estate prices in California this next example I thought we would get away from that large singing purple dinosaur but I guess not yet so why is it that we're needing a piece of pizza you're more likely to get your palate burned by the cheese on the pizza than the crust okay when both the cheese in the crust are at the same temperature well once again it has everything to do with the high specific heat capacity of water both the cheese in the crust were at the same temperature that's true but the cheese hasn't much higher specific heat capacity than the crust because of the water and oil in it so when that pizza is in the oven it's absorbing it's absorbing energy to reach its final temperature but the cheese portion of the pizza has absorbed a whole lot more energy than the crust because of the higher specific heat capacity now when you take it out of the oven and you put it in your mouth which is at a lower temperature than the pizza now for exactly the same reason as the water of the ocean behaves as this huge storehouse of energy that can now release that energy - okay the atmosphere in the same way the cheese on the pizzas behaved as this wizard war of energy and can now start releasing it to your mouth with the pasta ability of burning your parent and finally why is it that water is such an effective coolant in radiators of autumn of villages well if you think about what is the purpose of the radiator it is to be able to get rid of heat so that the your engine its temperature does not get high enough to actually melt okay the metal that it consists of so in the process of combusting the fuel a lot of heat gets released okay into that engine and the water behaves as a coolant it absorbs okay that heat from your engine because of the high specific capacity of water the high thermal insensitivity that means that it can absorb a whole lot of water without raising its temperature too much you certainly don't want to get the water in your engine to boil okay so water can absorb a lot more energy okay before reaching that boiling temperature then many other substances can because of its thermal instance set to insensitivity so that makes water and effective coolant it absorbs the energy so that the engine is your engine temperature the temperature of your engine never gets high enough okay to actually cause the breakdown of the materials that it's made out of so finally we'll talk about this process that we call calorimetry so what is it calorimetry is the process in which specific heat capacities and energy changes associated with physical care chemical processes okay it can be measured by placing objects in thermal contact and calorimetry these objects are placed in thermal contact in what we call a calorimeter which is nothing more than a thermally insulated container okay where we allow the calorimetric process to take place there's two types of calorimeters okay there's the cheap type that we call the coffee cup calorimeter which is really nothing more than a coffee cup believe it or not a polystyrene cup is is a good thermal insulator and with this type of calorimeter we have the contents inside which are exposed to the atmosphere so the prot whatever process is taking place inside of there whether it's a chemical or physical change it's taking place at constant pressure because like I said it's exposed to the atmosphere certainly the volume of the contents are allowed to change in this process okay let's compare that to what we call the bomb calorimeter certainly a more sophisticated type of calorimeter where we have a a closed thermally insulated container where the volume is kept constant so the process takes place inside okay and a constant volume but you can clearly imagine that for the energy changes taking place okay if if there is an increase in energy okay due to the process and an increase in temperature there's also going to be an increase in pressure so the pressure would be a quantity would change in this type of calorimeter so calorimetric theory is based entirely on the law of conservation of energy okay the conservation of energy principle so when it comes to problem solving if you want to find for example the specific heat capacity of a particular substance or you want to find the temperature change of a particular substance using a calorimetric get process then we say that when two objects at different temperatures are placed in thermal contact okay the heat that will be lost by the hot object must be exactly equal okay in magnitude to the heat that gained by the cold object so you see where the law of conservation of energy comes in okay that we can we use the symbol capital Q for heat so Q lost by the hot object okay well we will say is equal and opposite to the heat gained by the cold object because when we define a temperature change we typically define it to be the final temperature minus the initial temperature so the object that loses heat will end up at a lower temperature than it starts out with and have a negative temperature change whereas the object that gains heat okay the colder object to start out with will end up but a higher temperature than it starts out at in which case it will have a positive value for a temperature change so that's where we need the negative sign here we can write it like this if we want we can say that the Heat lost by the hot object plus the heat gained by the cold object okay it must equal zero it's a statement of energy conservation and using okay the singsong version here for okay how we determine how much heat gets transferred to or from an object q equals MC delta T I'll use the subscripts H for hot and c for cold okay so the hot object loses heat so okay you know massive hot object times the specific capacity of an object times its change in temperature plus the same for the cold object must equal zero okay and we can I'm just going to write when it comes to the temperature change here when we place objects in thermal contact they will both end up at the same final temperature remember that's what thermal equilibrium is all about okay heat will flow from the high temperature object to the low temperature object until both are in thermal equilibrium until both end up at the same temperature so you see here that the final temperature okay here of the hot object and the final temperature the cold object will be the same even though they're starting temperatures the initial temperature of the hot object and the initial temperature of the cold object we'll be different now in this next example we're going to use calorimetry theory to determine the composition of a coin so the problem goes something like this it says that an ancient coin is unearthed from a construction site to determine its composition and the calorimetry experiment is performed the coin having a mass of twenty seven point two grams is slowly heated in the calorimeter after adding a hundred and twenty-three joules of heat to the coin it's temperature rises thirty five point two degrees Celsius assuming the coin is a pure substance determine what it is likely made of now we can perform a calorie immature experiment and if we can determine the specific heat capacity of that coin knowing that it's a pure substance we could then look up our value in a table and try to match that and try to find out what substance it's composed of so we're going to start by identifying what information we're given in the problem what information is needed what information we trying to find and here notice that we're given the mass of the coin in this case unlike the last problem we're actually given the amount of heat added in this calorimetry experiment and once again we're told what the change in temperature of the coin is after the heat is added to it in this problem we're trying to find the specific heat capacity the specific heat capacity of a pure substance is unique and the table will show you that if you can find the value for C you can identify what the substance is made out of just like density the specific heat capacity is then becomes an intensive property of matter so knowing what we're given and what we're trying to find we can use our equation Q equals MC delta T we need to find C so let's solve it for C okay and when we plug in the numbers the 123 joules is the amount of heat that's added to the coin the mass of the coin twenty seven point two grams and the change in temperature of thirty five point two degrees Celsius when we do the number crunching we come up with this value of about point one two eight joules per gram degree Celsius okay the next thing we want to do is we want to go to our table and we want to compare values let's see what substance has a specific heat capacity as close as possible to 0.12 eight joules per gram degree Celsius and when we look at that table we see a high gold okay is very very close having a values about 0.129 joules per gram degree Celsius so although this doesn't prove beyond a definitive doubt it this it does tell us that this coin is very likely composed of gold so in this example we're going to determine how many calories are in a doughnut and you'll see how calorimetry can be used to determining the these caloric values that you find on the back of food packages we need to look at the back of a food package do you ever wonder where those values come from what it tells you how many calories are in a serving of the type of food you're eating okay well it's done by performing a calorimetry experiment using a bomb calorimeter so the data given to this problem a donut is dehydrated so the water is taken out it's been burned in a bomb calorimeter so that all the thermal energy released from the burning donut effectively heats up the water we're told here the 2.75 liters of water is heated from room temperature about 20 degrees Celsius in this case to 95 degrees Celsius and from that information we want to determine how many food calories are contained within that donut so we need to remember the whole basis of the calorimetry is were saying that the amount of energy that okay was in that donut okay left the donut in the form of heat and entered the water okay in the form of heat so the energy lost by the dome was exactly equal to the energy gained by the water in the calorimeter this is the basis of calorimetry so too we need to start by figuring out the mass of the water that was heated notice here that we're given the volume of water not the mass so if we want to use you know cubicles MC delta T we need to find the mass of water heated so we will convert get the volume of 2.75 liters okay using the density of water being about one gram per milliliter and converting okay leaders to milliliters we find out that we have two thousand seven or fifty grams of water being heated okay we can now find the change in temperature of the water by subtracting right so the water or the calorimeter starts out at room temperature of 20 degrees Celsius and in 95 degrees Celsius that corresponds to a seventy five degrees Celsius change so once we know the specific heat capacity of water we are now in a position to okay figure out how much heat got transferred to it so we're gonna multiply the mass times specific heat capacity of water for home one eight joules per gram degree Celsius times the temperature change of the water this tells us that 862 thousand joules of energy okay got added to the water in the form of heat now if we want to convert this to food calories okay using the mechanical equivalent of heat we know that 4180 joules okay is equivalent to 1,000 calories or one food calorie or okay large calorie using that conversion we find out that this was a 206 calorie doughnut not bad for a doughnut there must have been a small doughnut you know if not I got to get me some of those so the last example we'll take a look at in this video also involves calorimetry this is a slightly more complicated example and I'll say that I would normally do this in front of students and face-to-face format okay but given the fact that we're in a remote setting I won't be able to collect the data in real time okay but we will use our friendly lab equipment here to be able to help us do something rather interesting which is to estimate the temperature of a Bunsen burner flame now you can't just go stick in a typical thermometer in the flame of a Bunsen burner okay because it will ruin the thermometer okay this thermometer is not designed to withstand a temperature like this like that so we will use a calorimetry experiment we will use the law of conservation of energy to be able to safely measure the temperature of that Bunsen burner flame so let's take a look at the procedure with the help of some friendly lab equipment starting with our electronic balance what we're going to do is we are going to measure the mass okay of some water in our calorimeter we can use the tare button so the balance will tell us exactly what that mass is okay and I will tell you what that mass is on the next slide when we talk about all the data so we know the mass of the water in our calorimeter okay next we will okay with the help of theof the thermometer we will measure the temperature of that room-temperature water in the calorimeter notice that Theo is smiling there because the temperature of the water is just room temperature and he's taken an ice bath okay nice and comfortable next we are going to use the ball and ring apparatus we're going to unscrew the ball okay which is made of copper and mass the copper of all on our balance so we'll know the mass of the copper ball okay which we are eventually going to insert into the calorimeter cap once we've done that we're now ready to start the heating process there is Betty burner notice she is all warmed up and ready she's got a nice blue flame and we are going to now stick the ball and ring apparatus the copper ball in the blue flame and we will leave it there long enough until firmly Librium is established between the ball and the flame so after some time that ball is going to glow red and we can assume that the temperature of the copper ball will be exactly equal to the temperature that Bunsen burner flame so we will remove the ball and ring we will quickly insert the copper ball into the calorimeter cup okay stirring occasionally we will note that the temperature is going to increase and we will record the peak temperature okay of the mixture that is the water with the copper ball inserted so let's do that okay let's quickly insert the copper ball into the calorimeter cup temperatures rising and you'll notice the Theo okay is looking pretty hot there and like I said we will record Theo's peak temperature and we will write that on the next slide so in this slide we will record the data okay that we took from our experiment okay in the previous slide so let's take a look here we have our hot object okay our high temperature object which starts out okay being the ball and our cold object will be the water that's in our calorimeter music our coffee cup calorimeter to be exact and these quantities on the Left ok the mass the specific heat capacity the initial temperature of the final or equilibrium temperature these are the quantities that we need to find in order to solve this problem so mass in grams the copper ball had mass of 78.3 grams in the mass of water in the calorimeter was 122 point 1 grams a specific heat capacity of copper if you look it up this point three eight seven and for water it's four point one eight remember we said that metals have much lower specific heat capacities in water okay water is much more thermally thermally insensitive has a much higher thermal inertia the metals to the initial temperature of the copper ball that's what we're trying to fly okay we're assuming that when we place that comfortable in the calorimeter its temperature was the same as that of the Bunsen burner flame so that's our big unknown in this experiment the cold water of theö measured its temperature to be twenty-three point three degrees Celsius and the final temperature of the water that is our equilibrium temperature after okay the water and the copper were the same temperature that is when thermal equilibrium was reached okay that final temperature of both the copper ball in the water is fifty-seven point two degrees Celsius so now that we have conducted the experiment and we have our data we are now ready to analyze the data okay perform the calculations in order to determine the temperature of that Bunsen burner flame so remember the calorimetry theory is based on the law of conservation of energy simply that the amount of heat lost by the hot object will be exactly equal in magnitude opposite and sign - the amount of heat that is gained by the cold object the hot object was a copper ball ball the cold object was the water in the calorimeter so we're assuming that there was no heat loss to the environment okay in our calorimeter so here okay using our equation the heat loss by the copper ball would be the mass of the copper specific capacitive copper times the changing temperature of the copper ball and likewise for the water on the right-hand side of the equation remember the negative sign comes from the fact that okay the copper ball will end up at a lower temperature so it's delta T value will be negative okay whereas the object that is gaining the heat in this case the water will have a positive value of delta T so in order to reflect the fact that each of these objects has different signs of delta T we need that negative sign plugging in our numbers here from the previous slide okay filling in the data our only unknown is the temperature of the flame that is really the initial temperature of the copper ball and we do the number crunching we solve this equation we find out that the flame temperature is 600 and 28 degrees Celsius Susi clearly couldn't just go stick in a thermometer in a 628 degrees Celsius flame okay but using a calorimetry experiment we can figure this out pretty pretty easily and I would say that you know the the temperature of Bunsen burner flame is variable certainly that when I flame is red its temperature is gonna be much much less in this but when it glows blue you end up with that blue flame this temperature is going to be somewhere between 600 and 700 degrees Celsius