For more information, please see full course syllabus of High School Physics

For more information, please see full course syllabus of High School Physics

### Intro to Temperature & Heat

- All atoms and molecules have some vibrational motion in them, even solid objects. We call the average of this motion in a substance
*temperature*(T). - Since temperature is based on motion, the lower limit of this is when the objects stop moving: this is called
*absolute zero*. - We measure temperature in
*kelvin*(K). Absolute zero is 0K. One kelvin is the same "size" as a Celsius degree, but they have very different starting points. We can convert between them withT _{C}= T_{K}− 273.15. *Heat*(Q) is the__transfer__of thermal energy. Heat is__positive__when the environment puts thermal energy into the system, and__negative__when the environment takes energy out.- One
*calorie*(cal) is the amount of heat required to raise one gram of room temperature water by one kelvin/one degree Celsius. - Since thermal energy is a form of energy, we can covert calories to joules:
1 cal = 4.1868 J. - Different materials take different amounts of heat to have the same change in temperature. The
*specific heat*(c) of an object tells us the proportion of heat to temperature change. Different substances have different specific heats. - The more mass an object has, the more thermal energy it takes to increase its temperature. In general, the amount of heat required for a change in temperature is
Q = cm(∆T).

### Intro to Temperature & Heat

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Absolute Zero 1:50
- Absolute Zero
- Kelvin 2:25
- Kelvin
- Heat vs. Temperature 4:21
- Heat vs. Temperature
- Heating Water 5:32
- Heating Water
- Specific Heat 7:44
- Specific Heat: Q = cm(âˆ†T)
- Heat Transfer 9:20
- Conduction
- Convection
- Radiation
- Example 1: Converting Temperature 13:21
- Example 2: Calories 14:54
- Example 3: Thermal Energy 19:00
- Example 4: Temperature When Mixture Comes to Equilibrium Part 1 20:45
- Example 4: Temperature When Mixture Comes to Equilibrium Part 2 24:55

### High School Physics Online Course

### Transcription: Intro to Temperature & Heat

*Hi, welcome back to educator.com. Today weâ€™re going to be talking about temperature and heat.*0000

*All atoms and molecules have some vibrational motion in them. Theyâ€™re shaking around just a slight amount. Even solid objects still have some of this motion.*0005

*Well we canâ€™t see this motion without eyes, it is happening on an atomic level. This vibration has a huge impact on how substances interact with one another and how they behave on their own.*0015

*What do we call this slight shaking motion thatâ€™s so integral in the very nature that chemistry behaves?*0024

*We call it temperature. This is a strange thing at first but itâ€™s that motion, that slight shaking motion that is heat.*0032

*That is heat actually being something thatâ€™s slightly different that weâ€™re about to talk about.*0040

*That is what is warm, that is why something feels hot or something feels cold is how much of this shaking that is.*0044

*We call the average of the motion is in a substance, the average of this microscopic atomic level motion in a substance, temperature.*0051

*You denote it with the t. Note, this is the average of many different microscopic, super microscopic, not the sort of microscopic that you can see with a microscope, but something on the super micro level.*0058

*This is the average of many different tiny, tiny motions. On a macro level it seems like the substance is one unified temperature.*0070

*On a micro level one molecule might be moving slightly faster or slower than the next.*0079

*So on a micro level each one is moving slightly different than all of its neighbors, but when we look at the giant scale, weâ€™re seeing so many things happening at once.*0083

*We just take the average because thatâ€™s what it seems like to us because theyâ€™re so many tiny particles in there each doing slightly, slightly different behavior.*0091

*From our point of view we canâ€™t notice the tiny particles. Itâ€™d be talking about a beach but trying to talk about every single grain of sand.*0099

*We just sort of notice it as sand under our feet supporting us on the whole.*0106

*With this idea of temperature being based on super microscopic motion, we can see that there has to be a lower bound to that temperature.*0111

*When molecules completely stop moving we canâ€™t get below the point where they arenâ€™t moving.*0118

*Thereâ€™s no stiller thing than just being motionless. So once their motionless weâ€™ve gone down as far as temperature can go.*0124

*We call this lower limit absolute zero and itâ€™s going to form the base of our temperature scale.*0131

*The base of our temperature scale will be the lowest that we can get to, the lowest amount of motion we can have as nothing as so zero is nothing.*0136

*What scale are we going to use? For length we use meters. For mass we use kilograms. What do we use for temperature?*0145

*So far weâ€™ve talked a lot in terms of centigrade. Weâ€™ve talked about change, centigrade is actually Celsius, weâ€™ve talked about a lot of things in terms of Celsius and what is that?*0153

*Well kelvin is actually what weâ€™re going to switch over to. Weâ€™re going to have a starting point for temperature and now we can introduce temperature measurement and weâ€™re going to use kelvin.*0163

*So kelvin is the exact same size, the distance on a kelvin from 0 to 1 and 1 to 2. Itâ€™s the same thing.*0172

*One change in a kelvin degree is the same thing as one change in a Celsius degree.*0181

*There are still 100 kelvin degrees to get from the frozen point of water to the boiling point of water; I mean the end of the frozen point to the beginning of the boiling point.*0185

*Itâ€™s not going to start at the same place so Celsius has its zero set at frozen water, a reasonable thing when youâ€™re living in normal daily life.*0195

*When you want to do laboratory experiments, youâ€™re going to want to have it set down so your kelvin is set at zero, is set at the very base of where temperature can go.*0204

*Itâ€™s going to matter a lot when we talk about certain other things later on.*0213

*The Kelvin scale is 0k is absolute zero. 0 degrees Celsius on the other hand is a freezing point of water at 1 atmosphere of pressure.*0216

*To convert between the two we have the temperature in Celsius is equal to the temperature in kelvin minus 273.15.*0225

*If you want to go from kelvin to Celsius, you just add 273.15 and youâ€™ll get what youâ€™re numberâ€¦sorry, if you want to go from kelvin to Celsius, you subtract.*0232

*If you want to go from Celsius to kelvin then youâ€™re to add 273.15 because you need to get from the fact that your 0 of frozen water is actually 273.15 above where the stopping of motion is or the end to temperature is.*0240

*I think itâ€™s kind of the end. Heat versus temperature. In everyday life we often talk about heat and temperature as totally interchangeable ideas.*0260

*I accidentally slipped up and did it at the very beginning of this lesson in fact.*0269

*In physics we make a distinction, heat we denote it with a q. Heat is the transfer of thermal energy.*0273

*Heat is positive when we put thermal energy into a system and itâ€™s negative when the environment takes it out.*0280

*So environment puts it in, youâ€™ve got positive heat, positive q, positive thermal energy.*0287

*Its negative when the environment takes it out. So if the system gets cooler, itâ€™s going to be negative heat, itâ€™s going to be a heat flow out of it. Itâ€™s going to be negative thermal energy, negative q.*0293

*Notice the similarity to work in energy. When we were dealing with energy, energy was the fixed quantity that moved up and down.*0304

*Here temperature is the fix, once again these things arenâ€™t really fixed, they clearly move around a lot.*0311

*But temperature was the thing that moved up and down based on how much work we put in.*0315

*Positive work when we put energy into the system, negative work meant we took energy out of the system.*0318

*Itâ€™s the same thing here, positive heat, positive q means that we put thermal energy into the system. Negative q means we take energy out of the system.*0324

*Itâ€™s the exact same thing. If we want to heat stuff, how much heat do we have to put into it?*0331

*If we want to heat water, if we want to say raise the temperature on a pot of water, how much heat do we have to put in to it?*0337

*Clearly from experience the more water in the pot the more heat we need to raise. If you have a small pot of water itâ€™s going to boil way faster than if you have a giant, giant pot of water.*0343

*Weâ€™re used to this at this point. Clearly the amount of the object, the mass of the object is going to have some effect on it.*0352

*Thereâ€™s also some other stuff coming into it. For water, one way to measure that heat is the calorie, which is shortened to Cal when weâ€™re putting it in as a unit.*0359

*1 calorie is the amount of heat required to raise 1 gram, and notice thatâ€™s gram, not kilogram.*0369

*1 gram of room temperature water by 1 kelvin or 1 degree Celsius.*0377

*If youâ€™re at room temperature and you want to increase the temperature by 1 degree Celsius or kelvin, not Fahrenheit.*0382

*If you want to increase it by 1 degree, you put in 1 calorie. If you have 1 gram, 1 degree gets 1 calorie.*0390

*Thermal energy is just energy though, so we can also use the joule, the conversion between calories and joules is 4.1868 joules to the calorie.*0397

*Thatâ€™s a defined thing because the calorie, the amount of energy, the specific amount of energy that youâ€™re going to have to put in to get a temperature raise of 1 degree actually varies a little bit as the temperature of the water goes up.*0408

*For our purposes, weâ€™ll be perfect fine to call it one calorie, but notice there is a very slight change as we move around. As we get farther and farther away from room temperature.*0418

*One calorie wonâ€™t be quite enough to make the exact same change. If we want to be really precise scientist is able to use joules instead because calorie is defined to make 4.1868.*0427

*Having it mean 1 calorie havingâ€¦for 1 calorie to heat 1 gram, 1 degree isnâ€™t going to always be the case.*0441

*Itâ€™s actually more correct to base it just on ideas of energy and then weâ€™ll have to do lots more specific measurements if we want to be really careful about this.*0450

*For our propose we can treat it as always being 1 gram, 1 degree. Specific heat, the amount of heat needed to raise one objects temperature is going to be different than the amount of heat needed to raise another objects temperature.*0459

*Water is different than steel is different than wood is different than granite is different than rubber.*0473

*Each one of these is going to need different amount of heat. Theyâ€™re going to have a different heat and thatâ€™s based on the chemical composition and the really deep molecular atomic structure of these things.*0478

*Thatâ€™s something we defiantly wonâ€™t be getting into. Just for our proposes, itâ€™s enough to know that thereâ€™s going to each oneâ€™s going to need a different coefficient.*0487

*We define this coefficient as specific heat, c. That will give us some proportion; this proportion is going to vary based on the substance.*0495

*Weâ€™ll have to get it for each problem or look it up in a table if we want to find out what it is.*0503

*We are able to look these things up and then figure out how much heat energy weâ€™d have to put in to an object.*0508

*The amount of heat needed for a given mass, m, to have a temperature change, delta t, is given by the equation q, the heat we put in, is equal c, thatâ€™s specific heat, times the mass of the object times the change in temperature.*0512

*This makes a lot of sense. Each objectâ€™s going to have a different type, c, different amount proportion for their heat that they need.*0526

*Each thing is going to care how much mass it is. A small pot of water takes a different amount of time than a large pot of water.*0534

*Thereâ€™s also going to be a big difference if you want to raise the temperature in that water just a little bit or if you want to get it all the way from frozen ice to boiling water.*0540

*Totally different numbers are going to be needed in each one of these and so we take account with that with c for the proportion, m for the mass, the amount of the thing and change in t, the delta t for just how much we want to make a difference in the temperature.*0548

*Heat can be transferred through one of three of methods.*0561

*The first one is conduction. Direct contact, motion in the atoms is directly passed to adjacent atoms. If I heat one end of this pencil, pen, Iâ€™m not really sure what to call it since it writes on a tablet, but if I were to heat one end of this, over time that would heat would slowly make it way through the object, all the way through.*0565

*Some things are going to conduct heat at different rates. Youâ€™ve probably see this before if you use a wooden spoon to stir a pot, the heat gets transferred to the end of that spoon way slower than if you use a metal spoon.*0583

*Theyâ€™ve got different rates of conduction. One again thatâ€™s going to be based on the chemistry involved. A really good example would be if we were to put an empty pot to heat on a stove, so if we just put an empty pot and heat it on the stove.*0595

*This isnâ€™t a good idea to do at home because it probably wonâ€™t hurt you but it is going to possibly ruin a nice pot. If you were to heat an empty pot on the stove though the temperature, either the hot coils or the hot gas flame would heat the bottom of the pot and that heat would spread through the metal.*0606

*It would be spread directly through conduction. The next one is convection. This is fluid motion doing the work. A combination of fluid motion happening and conduction.*0624

*If a fluid manages to have a hot pocket and then that hot pocket gets spread through, itâ€™ll manage to conduct way faster than if itâ€™s trying to conduct layer through layer through layer.*0636

*Itâ€™s a combination of direct conduction and the fluids mixing due to pressure differentials from temperature variation.*0645

*Hotter water has a slightly different pressure than colder water so that hot water is going to rise which means that itsâ€™ going to spread out through the colder layers that are now above it and itâ€™s going to spread it and it weâ€™re going to get convention currents.*0651

*If fire at the bottom of a chimney, itâ€™s going to heat the air directly above it. That hot air will rise and will now easily touch the air at the top of the chimney making it hotter.*0664

*Its not direct conduction, itâ€™s not having to make it through each layer of air atoms. Itâ€™s that itâ€™s heating the hot air and then that hot air has a different amount of pressure in it.*0674

*So that gust of hot air, that packet of hot air will move up the chimney and it will manage to mix with the colder air at the top and so it will heat that hot air more easily.*0683

*Finally, radiation, electromagnetic waves. Hot objects emit EM waves that can be received by other objects increasing their internal thermal energy.*0695

*Great example of this would be to go out on a sunny day. That sun, the reason that you can feel any heat from that sun is because of electromagnetic waves.*0704

*That sun doesnâ€™t have anything to conduct through. It doesnâ€™t have convention. Itâ€™s got the dead vacuum of space for a long distance between us and it.*0711

*The only way that heat manages to make it to us is because itâ€™s able to directly shot it at us.*0719

*It uses light to shot it at us. Infrared is one of the main carries of heat energy, as one of the first thing that a hot object starts to emit.*0723

*Its also going to emit it through a variety of spectrums. If youâ€™ve ever heard of something being white hot, thatâ€™s because itâ€™s literally been heated to the point where it manages to emit white light.*0731

*When something is red hot itâ€™s at less energy because itâ€™s only emitting a lower wave length. Itâ€™s emitting red which is less than the entire spectrum.*0740

*White light being the entire spectrum of light seen a once. When we manage to make something really, really hot temperature, if youâ€™ve ever seen a glowing piece of steel either in a movie or in real life thatâ€™s because itâ€™s so hot it actually managing to broadcast light to us.*0748

*Thatâ€™s what happening to the flame too. That thing is so hot itâ€™s managing to broadcast light to us.*0766

*Itâ€™s not able to take anyone of these on its own. That fire at the bottom of chimney, itâ€™s able to heat some of those bricks at the top of the chimney by directly shooting electromagnetic waves at them.*0773

*Which is then also going to be able to conduct to the air next to it. Anyone of these, theyâ€™re going to come together.*0785

*You canâ€™t just say thereâ€™s just one at a time because theyâ€™re all working together. Theyâ€™re all working in concert.*0790

*Each one works slightly differently and itâ€™s an interesting to have an understanding of how heat is moving around.*0795

*Weâ€™re ready for some examples. If we had a block of steel that had a temperature of 540 kelvin what would that be in Celsius?*0802

*Remember, the temperature in kelvin minus 273.15 is equal to the temperature in Celsius.*0808

*Interesting point about kelvin is when we talk about kelvin we donâ€™t say degrees kelvin. We just say number kelvin.*0819

*So 540 kelvin. When we talk about Celsius though we say degrees Celsius.*0824

*Itâ€™s just a thing that we do, itâ€™s the way we describe it.*0830

*If a block of steel is the temperature of 540 kelvin, how do we convert that?*0834

*Well weâ€™re going to need to move that down because kelvin has a higher number for this same temperature.*0838

*We move that down 540 subtract by 273.15, we get 266.85 degrees Celsius.*0844

*If on the other hand weâ€™re going from -15 degrees Celsius, if we had a cloud of air at -15 Celsius and we needed to know what that was in kelvin.*0854

*We would add that same amount 273.15. So we add 273.15 and we get 258.15, no degree mark, just kelvin directly.*0862

*If weâ€™re got something thatâ€™s in kelvin and we need to convert it to Celsius the number we get lower because kelvin has a lower starting base.*0875

*If we have something thatâ€™s in Celsius and we convert it to kelvin the number will get higher because Celsius has a higher starting base.*0885

*The number that we convert with is 273.15.*0891

*A calorie in food, notice the capital C. This is an interesting point, a calorie in food, if you look at the back of a box.*0896

*If youâ€™re in the United States, Iâ€™m not quite sure about some of Europe. But if youâ€™re in the United States and you see a calorie of food youâ€™re going to see that itâ€™s not actually the same thing as the calorie we were talking about.*0904

*We see calories on the back. Other countries though will actually stop kilocalories because what a calorie is with a capital C is itâ€™s actually a kilocalorie.*0917

*Itâ€™s 1,000 of those calories that heat water that we were talking about before.*0927

*Some countries in fact, they donâ€™t need calories because they could also just talk about in straight energy.*0931

*Other countries will use joules on the back. Weâ€™ll talk about the kilojoules that the food has that youâ€™d be looking at.*0934

*Itâ€™s an interesting point of view. Itâ€™s an interesting point; we couldnâ€™t look into this as anything as long as weâ€™re looking in terms of the energy that one of these things can impart.*0940

*If weâ€™ve got calories, as kilocalories, and a person burns 2,000 kilocalories in a day. Whatâ€™s their average power output going to be?*0948

*Remember we had 1 calorie is equal to 4.1868 joules. SO what would one kilocalorie be?*0957

*It would be 1,000 times that. If we want to see the energy of the kilocalorie is then weâ€™ve got 2,000, sorry energy of 2,000 kilocalories.*0968

*Thatâ€™s what we want to look at, the 2,000 kilocalories from here. So energy of 2,000 kilocalories is going to be 2,000, the number of kilocalories times 10^3 because weâ€™ve got a kilo, weâ€™ve got a 1,000 of them, calories.*0982

*The conversion between calories, so at this point weâ€™ve got 2,000 times 10^3 plain calories.*0994

*If we want to convert it to joules we multiply by another 4.1868 and this will tell us what the number of joules is in 2,000 kilocalories.*0998

*We get, multiply it out, and we get 8.374 x 10^6 joules.*1007

*The person goes through 8.374 x 10^6 joules in a day. If we want to know what the power is, we need to figure out how many joules you go through per second.*1018

*So what would be the average output over the day? Well itâ€™s going to be power is equal to the change of energy, the amount of energy we use, this number right here.*1026

*Divided by the amount of time. Well the change in energy, weâ€™ve already figured that out, we use up 8.374 x 10^6, at least for this average person using 2,000 kilocalories a day.*1036

*Not necessarily average the amount that you need, depends on your personal lifestyle, your personal metabolism, and how much work you had to do.*1049

*On a cold day, a linebacker, a heavy athletic person. On a cold day practicing can use something like 6,000 calories in a day.*1058

*If youâ€™re living...if youâ€™re a very small person, living in a warm climate, you might only need 1,500.*1066

*It depends on your personal life. 8.374 x 10^6 joules, we want to divide that by, well how many hours are in a day?*1070

*24 hours in a day. How many minutes in an hour? 60 minutes an hour. How many seconds in a minute? 60 seconds.*1078

*We put that all the together, we divide it out and we get 96.92 watts.*1084

*Thatâ€™s what the person average power output is. Keep that in mind, think about that.*1092

*A watt, a bulb where used to using a 100 watt bulb to light our house. If you have incandescent bulb at 100 watts, that things actually pretty warm to the touch.*1097

*It can burn you. Thatâ€™s how much heat your body is putting out pretty much. Your body is going to be putting out almost certainly at least 96.92 watts at any time.*1106

*Thatâ€™s why a crowd of people, if youâ€™ve ever noticed that itâ€™s a cold day but youâ€™re standing with a crowd of people its noticeable warmer.*1116

*Or if youâ€™re in a closed classroom for a long time. It starts to get noticeably hot. Part of that is just because of the raw amount of heat that a bunch of bodies sitting around make.*1123

*A bunch of live people put out a lot of heat. Thatâ€™s what youâ€™re seeing, youâ€™re actually seeing waste heat of a bunch of people just standing around.*1133

*Granite. Granite has a specific heat of .79 kilojoules; notice this is kilojoules, not joules.*1142

*If you have a 2.5 kilogram block of granite currently at temperature 280 kelvin and you want to raise the temperature by 20 kelvin, how much thermal energy needs to be put in?*1149

*First off, Iâ€™d like to point out; do we need to know what the starting and ending was if we know what the proportion is?*1158

*If we know what the specific heat is for the level weâ€™re starting at, we donâ€™t actually need to know the temperature.*1164

*We know weâ€™ve got 280 kelvin going to 20 kelvin, so we end at 300 kelvin, but the important thing is the change in t is equal to 20.*1169

*Thatâ€™s all that we really care about. If change in t equals 20, c is equal to .79 kilojoules per kilogram times kelvin and 2.5 kilograms is the amount of our mass, then we have q is equal to the specific heat times the mass times the change in the temperature.*1177

*We plug everything in, ah .79 kilojoules, so if we want to do this in joules, what weâ€™re used to doing.*1193

*Weâ€™ll want to change it to kilojoules with .79 x 10^3. So itâ€™s joules per kilogram per kelvin.*1199

*We multiply by the mass, 2.5 kilograms times the change we want to effect. So we want to change 20, we put it all together and we get 39,500 joules.*1208

*If we were curious how many kilojoules that would be, we just divide by 10^3, move that decimal over by three, 39.5 kilojoules.*1221

*Either way you want to look at it, same thing.*1230

*You use the specific heat that youâ€™ve got, the mass that youâ€™re working with and the temperature change. Put them all together and that tells you how much heat needs to be put in to get the change.*1234

*Finally, we have a perfectly insulated, this means the environment wonâ€™t effect it so we donâ€™t have to worry about it radiating heat or heat being put in from the environment.*1246

*We know that we only have to care about whatâ€™s happening inside. Weâ€™ve got a perfectly insulated container that is 4 liters of water at 10 degrees centigrade.*1255

*You place a 3 kilogram brick of iron that is currently at 400 degrees centigrade, whoops typo right here. This should be 400 degrees centigrade, into the water.*1262

*Of the specific heat of iron is .47 kilojoules per kilograms times kelvin. What temperature will the water/iron brick mixture be when it comes to equilibrium?*1272

*First thing, do we have what the mass of water is? We donâ€™t have it yet actually but one more thing that we havenâ€™t mentioned before.*1283

*What you might have learned in pervious science classes, is that 1 milliliter of water, so 1 milliliter of water is the same thing at most pressures and most temperatures.*1291

*1 milliliter of water is the same thing as 1 cubic centimeter of water, which is the same thing as 1 gram of water.*1301

*Thus, 1 liter has got to be 1 kilogram since there is 1,000 milliliters in a liter and there is 1,000 grams in a kilogram. Then we know that 1 liter of water at normal temperature and pressure is what weâ€™re dealing with in this problem.*1315

*We know that weâ€™ve would have 4 kilograms of water for this problem. So the mass of our water is equal to 4 kilograms.*1328

*We know what the mass of the iron is. Do we know what the coefficient for the iron is? We know what the coefficient for the iron is.*1339

*Do we know what the coefficient for the water is? Well once again, we know that the coefficient for water is in general 1 calorie per gram per kelvin.*1344

*If we want to switch from calories to joules, we have 4.1868 joules per gram per kelvin and notice we couldnâ€™t do this if we were in calories because weâ€™ve got a different thing over here.*1357

*Weâ€™ve got a different thing for our iron, so weâ€™d have to convert into calories there.*1371

*We have to make sure that weâ€™re dealing with this same thing for both of them.*1375

*If we want to convert from joules per gram per kelvin into kilojoules per kilogram, well 1,000 but also divided by 1,000, so itâ€™s going to wind up being the exact same thing since its kilo both on the top and the bottom.*1378

*Kilojoules per kilogram times per kelvin. At this point, weâ€™ve got what the coefficient for water is.*1391

*We know what its specific heat is. We know what the specific heat of iron is.*1400

*One more idea, if we put iron into water itâ€™s going to conduct its heat both through, weâ€™re going to have conduct, weâ€™re going to have convection, and weâ€™re going to have electromagnetic waves bouncing around inside of that container.*1405

*What will be the final heat? Sorry, what will be the final temperature, not the final heat?*1421

*What will be the final temperature for that container? Are they going to have to agree on a temperature at the end? Yeah, when they hit equilibrium, thereâ€™s going to have to be at the same temperature otherwise theyâ€˜re going to continue transmit heat.*1426

*Only when something is at the same thing are they not transmitting heat back and forth.*1439

*What isâ€¦whatâ€™s that going to be? We know that the amount of energy we put into the water, the amount of thermal energy that gets put into the water because itâ€™s going to have its heat, itâ€™s going to have to take positive heat in because itâ€™s having its temperature raised.*1445

*Itâ€™s going to be the amount of energy that the iron loses. If the iron, itâ€™s going to have a negative amount because itâ€™s putting energy out of itself. Energy is coming out of it so itâ€™s going to have a negative heat.*1459

*That means that we need to change that to a positive for it to be the same thing as the water.*1472

*The amountâ€¦the total absolute amount of energy that the iron loses is the amount of energy that the water gains because weâ€™ve got this perfect insulator around it.*1478

*Negative heat becomes the positive heat of the water. This relationship right here is how weâ€™ll be able to solve this problem.*1488

*At this point weâ€™ve finally ready to work on it. Hereâ€™s all of the things we need.*1496

*The mass of water is equal to 4 kilograms. The mass of the iron is equal to 3 kilograms. The temperature of the water is 10 degrees centigrade. The temperature of the iron is 400 degrees centigrade.*1500

*The coefficient for the water is 4.1868 kilojoules per kilogram per kelvin. The specific heat for the iron is .47 kilojoules per kilogram per kelvin.*1510

*What is our ending temperature? We need to know that the amount of energy that goes in for a specific heat for the amount of heat that has to go in for a temperature change is going to be the specific heat times the mass times the change in that temperature.*1520

*One quick question, do we have to convert from Celsius into kelvin before we can do this problem?*1539

*In this case we donâ€™t actually have to do it because weâ€™re only looking at the change, the difference between those two numbers are going to be the same difference whether weâ€™re looking at this in kelvin or if weâ€™re looking at this in Celsius.*1545

*The difference between a Celsius, 1 Celsius and 1 kelvin is the same distance temperature wise.*1555

*If weâ€™re looking at the change in temperature, itâ€™s the same thing if we do it as 400 Celsius or 673.15 kelvin.*1562

*Ultimately when we look at the difference itâ€™s going to be the same difference whichever way we measure this to begin with.*1571

*We can actually continue to work in Celsius. We know that the change in the heat for the water is equal to the opposite of the heat for the iron because the iron heat is negative.*1579

*We set this two equal to one another and weâ€™ve got that c of the water times the mass of the water times the temperature difference.*1590

*We want to actually use the temperature difference because we want end to show up minus the temperature of the water is equal to negative specific heat of the iron times the mass of the iron times the ending temperature.*1600

*Its going to be the same ending temperature on both sides minus the starting temperature for the iron.*1613

*Letâ€™s start moving things around, make this a little bit easier. Weâ€™ve got â€“cimi x tn so we can multiply that in.*1618

*We distribute the right side and add it over here. Weâ€™ve got cwmw t end plus because itâ€™s negative on the right side, plus cimi t end.*1624

*Then weâ€™ll move everything thatâ€™s not t end based because weâ€™re solving for t end to the right side.*1643

*Weâ€™ve got cwmw x â€“tw, so we add that over here, we have cwmw tw and then over here that â€“cimi hits the negative t end, so we get positive.*1648

*So weâ€™ve got positives on both sides, cimi ti. Letâ€™s actually take a quick pause and look at this for a moment.*1662

*Notice what weâ€™ve got here. Weâ€™ve got cwmw t end plus cimi t end, so this the total inertia to speak.*1669

*The thermal inertia for the system as a whole, the iron and water together at the end is going to be the temperature times its specific heat times the amount of mass.*1679

*On the right side, weâ€™re going to haveâ€¦itâ€™s going to become aâ€¦weâ€™ve got what the total thermal inertia is here plus the thermal inertia here.*1689

*We know that the total amount of heat energy, sorry the total amount of thermal energy for the iron plus the water is going to have to be the same no matter what because we arenâ€™t losing any thermal energy because weâ€™ve got that perfect insulation.*1697

*The total amount of thermal energy at the beginning is going to be equal to the total amount of thermal energy at the end.*1712

*We start solving for t end. Pull out the t end, we have cwmw plus cimi equals all that same stuff over.*1718

*We divide by cwmw plus cimi, whoops I accidently got confused again, a lot of letters here.*1734

*Cwmw tw plus cimi ti all over cm, ah keep doing that. Cwmw plus cimi.*1747

*At this point Iâ€™d also like to point out what weâ€™ve basically got, is weâ€™ve got a weighted average. Weâ€™ve got a way of weighting how much the water temperatures matters because weâ€™ve got cw times mw.*1766

*What sort of that thermal block is like, how much mass it has along with its specific heat, to see how hard it is to push that mass around temperature wise.*1777

*Along with its starting temperature plus cimi ti, what its thermal inertia is, times that starting place.*1785

*Then we divide it, we average it, we have to take that out because we want to just get temperature at the end.*1793

*If you remember back to finding the center of mass, there is a lot of similarities to center of mass here.*1797

*What weâ€™re looking for in the end when we solve it out like this is weâ€™re really looking for the weighted average between these things is.*1802

*We have to work this out with algebra because itâ€™d be too easy to just go 400 plus 10 divided by 2 wonâ€™t be the correct answer.*1808

*Because weâ€™ve got different amounts of water then we have iron. Weâ€™ve got difference specific heats for water and iron. Weâ€™ve got to work this thing out with math, but it is going to be a weighted average.*1814

*Itâ€™s how important the heat, how important the temperature in that water is versus how important the temperature in the iron is and what it becomes when we put them together.*1823

*We finally substitute in a huge mess of numbers, we have cw is .47, now once again, what are we working with?*1833

*Weâ€™re working with kilojoules. So we probably want to switch to joules because we know joules are the friendly SI unit. Just in case weâ€™ll switch it over.*1844

*Weâ€™ll see in the end that wasnâ€™t going to be too important but weâ€™ll switch it over for now.*1854

*Specific heat of water, 4.1868 x 10^3 to deal with that kilojoules time the mass of the water, 4 kilograms times the starting temperature of the water, 10 degrees Celsius plus ci.*1857

*So .47, but once again weâ€™ve got kilojoules so we multiply that by 10^3 times the mass of the iron, 3 kilograms times the starting temperature of the iron, 400 degrees Celsius.*1873

*Then we divide that by 4.1868 x 10^3 x 4 + .47 x 10^3 x 3. Now at this point notice weâ€™ve got 10^3 showing up everywhere.*1887

*10^3 here, here, and here. SO every single one of our additive elements there had a 10^3 factor so we can cancel it out.*1906

*Ultimately in this case because we had this specific heat using the same unit on the top and the bottom and we had specific heat showing up everywhere weâ€™re able to completely cancel out that unit.*1915

*So that all that matter was the coefficient in front of that unit. Thatâ€™s a dangerous thing to do just like toss around so you donâ€™t want to just use unit without understanding what youâ€™re using.*1924

*Itâ€™s generally the safest thing to do is to use the SI unit, whatever it is.*1935

*Once again, thatâ€™s why we had to talk about why we were using Celsius instead of converting the kelvin first.*1940

*If we think about it, it might be the case that we can get away with using non perfect SI unit, but sometimes youâ€™re going to completely ruin your problem by thinking you can.*1944

*And you wonâ€™t be able because itâ€™s inherent in the way that the formulas we have, we have expectations.*1952

*We finally punch all this into a calculator and the number that we get out is 40.3 degrees Celsius.*1958

*40.3 degrees Celsius, notice how low that is. That iron block was almost the same mass of our water.*1968

*Almost the same mass as our water and it was 400 degrees Celsius when we put it into that water and yet we managed to raise the temperature of the water by 30.3 degrees.*1976

*Hardly anything. Thatâ€™s less than a 10th of the temperature difference to the block of iron.*1987

*Why is that? Because the specific heat of iron is so much lower than the specific heat of the water.*1993

*More accurately, itâ€™s because the specific heat of water is so freaking high. The specific heat of water is really, really, really high compared to most other things.*1998

*Most other things are at least below 2, if not below 1. The specific heat of water is really high number.*2009

*Itâ€™s actually one of the reasons that life can exist is because you can go out on a hot day and be basking in the sun and your body temperature wonâ€™t jack up because youâ€™ve got all that water to give you this nice thermal inertia that will keep you from moving suddenly from one temperature to another.*2014

*Itâ€™s one of the great things that make the possibility for life here on Earth. The fact that weâ€™ve got this wonderful stable water temperature because weâ€™ve got this wonderful high specific heat for water.*2028

*Really interesting. Hope you enjoy this, hope you learned something great and weâ€™ll meet again at educator.com later. Bye.*2041

1 answer

Last reply by: Professor Selhorst-Jones

Thu Mar 14, 2013 10:30 AM

Post by Adil Garad on March 13, 2013

There is a question on my homework sheet that I cannot figure out:

Q: "What mass of copper at 90'C, when added to 200g of water at 15'C contained in a 100g aluminum calorimeter, will give a final temperature of 20'C?"

I want to know how to include the calorimeter into the question. Can you show me the steps for solving this question?

Thank You.