welcome in a previous video we looked at different units of measurement things like volume and length and mass and the units associated with those measurements now we're going to look at two other units of measurement temperature and energy we're going to look at the units associated with each and we're going to look at how to do a simple experiment in which you can provide energy to a system you're going to measure the temperature difference where you start where you end and with the temperature difference and a conversion factor will be able to then calculate how much energy was used in achieving the temperature difference so let's look at units of temperature in the english or u.s customary unit the unit of temperature is degrees fahrenheit in the metric system it is celsius or centigrade in si unit international system of units the unit of temperature is kelvin now just to get a vague idea if you're measuring temperatures in fahrenheit um this is the freezing point of water this is the boiling point of water 32 freezing point 212 boiling point compare that to the metric system uh people developing the metric system chose these two critical points of the most important compound on earth water it's freezing point at its boiling point and define the centigrade scale because there's a hundred degrees centigrade between the freezing point of water 0 degrees celsius and the boiling point of water 100 degrees celsius that is how the celsius scale scale was defined now if you compare that to degrees fahrenheit the difference between the boiling and freezing point of water here is 180 degrees as opposed to only 100 degrees in the metric system so 1 degree celsius is almost twice as large 1.8 times as large as 1 degree fahrenheit all right now in science of course we use the metric system or occasionally bsi system the si system is as usual derived from the metric but all we do is to whatever your temperature is in degrees celsius we add 273 to it and that gives you your temperature in kelvin one of the nice things about the kelvin scale is that all values are positive that is below zero in celsius you go to negative values but this continues being positive all the way to zero degrees kelvin what we call absolute zero and we don't get temperatures below that so after that and that is of course minus 273 celsius and above that all the temperatures in kelvin are positive so now let's move to energy specifically heat a form of energy and the unit of energy that we're going to use which is the calorie let's first define what is a calorie if you have a drop of water which weighs one gram you have one gram of water and you provide enough heat to this water so that its temperature let's say initially was at 14 degrees celsius so that its temperature goes up by one degree celsius that amount of energy provided is one calorie so one calorie is the amount of energy needed to raise a temperature of one gram of water by one degree celsius now let's say that rather than having a gram of water we have one gram of kinetic white copper and again you start heating it and let's say initially the temperature was also 14 degrees celsius and let's say that you provide one calorie of energy to this one gram of copper the question is do you expect the final temperature to be 15 degrees greater than 15 or less than 50. and the answers it turns out is a lot more than 50 degrees celsius so why is that well think about being outside and on a hot summer day where the sun is providing the same amount of energy to everything on the surface of planet earth and let's say there's a little bottle of water and there's a slab of metal and you need to sit on one or the other um and you're thinking about not burning your rear end uh which one would you choose chances are you would choose the water because the water is going to be cooler than the metal the metal is going to be a lot harder for the same amount of energy provided by the sun so another way of looking at this is it took me one gram i mean one calorie of energy to raise a temperature of one gram of water by one degree celsius whereas for copper if i want that final energy to be 15 if for one calorie it's going to be a lot more than 15. i'm only going to need a fraction of a calorie to raise the temperature to 15 degrees so let that fraction of a calorie happens to be for copper 0.092 calories per gram per degree celsius it only takes the small amount of energy 0.092 calories to raise a temperature of 1 gram of copper by 1 degree celsius we call each of these the specific heat of a substance each element each substance has its own unique specific heat and so whether you're talking about jello or copper or water or wood each of them has its own specific heat and what is interesting about specific heat is that it ties together units of energy of heat two units of temperature so this specific heat is a conversion factor that will allow us to convert a temperature difference into energy so again specific heat is the amount of heat needed to raise a temperature of one gram of substance by one degree celsius and it is a conversion factor let's say that i have a certain mass of water on a pot and i set that on the stove and i start heating it so that an initial temperature of let's say 20 degrees celsius is raised to 50 degrees celsius okay now we're using water so i know that the specific heat of water is one calorie per gram per degree celsius if i do this calculation and let's come up with an easy mass let's say a thousand grams my grams will cancel with my grams my degree celsius will cancel with my degree celsius and at the end of the day with this simple equation i'll be able to calculate the number of calories right a thousand times 30 or 30 000 calories needed to raise the temperature of a thousand grams of water by 30 degrees celsius very nifty and you can see how we use this conversion factor the specific heat to convert a temperature difference into calories so here is the equation that we use heat in calories is a mass there's a specific heat of that substance times a temperature difference okay so now let's look at energy or more specifically heat a type of energy and the unit that we use to measure heat which is calories first we're going to define what is a calorie so let's say that we have one gram of water and this water is initially at a temperature of 14 degrees celsius and i'm gonna heat this gram of water with enough energy to raise the temperature of this one gram of water by one degree celsius all the way to 15 degrees celsius that is one calorie of energy one calorie of energy is the amount of energy needed to raise the temperature of one gram of water by one degree celsius all right now let's compare this to having one gram of a metal like water and let's say that my copper is initially also at 14 degrees substance now let's say that i start heating this copper and i provide one calorie of energy to this one gram of copper my question is will the final temperature of this copper be 15 degrees celsius more than 15 or less than 15. as it turns out final temperature temperature will be a lot more than 15 degrees celsius and you could probably have come up with this answer if you just visualized being outside on a hot summer day with the sun heating the surface of the place where you're at with the same amount of energy and let's say there's a puddle of water and a slab of metal and i ask you to sit choose which of the two you want to sit on chances are you're gonna choose to sit on the water because the slab of metal would burn your backside the slab of metal is going to be a lot hotter than the water so for the same amount of energy the metal temperature will go up a lot more than the same amount of water another way that i could write this is like this saying that it takes one calorie of energy to raise a temperature of one gram of water by one degree celsius or it takes a fraction of a calorie specifically 0.092 for copper to raise the temperature of one gram of copper by 1 degree celsius if i provide a whole calorie it goes up by a lot more than one so i only need to provide a fraction of a calorie for that temperature to go up by one degree celsius each of these quantities is unique to the elemental compound that we're talking about because it's unique it's a unique property and that property is called specific over substance the specific heat of a substance is the amount of heat needed to raise a temperature of exactly one gram of that substance by exactly one degree celsius and again it's a different number for water copper wood jell-o what not what is interesting here is that the specific heat ties together a unit of energy or heat to a temperature so this is inherently a conversion factor that would allow us to tie together energies to temperature now let's say that i'm doing an experiment i put in a pot of water um i put let's say a thousand grams of water and i start heating it because it's water i know that the specific heat is one calorie per gram per degree celsius and as i heat it the temperature that let's say initially was at 20 degrees ends up being 50 degrees celsius all right if we do this calculation where you can see that grams cancel out and degrees celsius cancel out i'm going to end up with calories the amount of energy that i needed to supply to raise the temperature of these thousand grams of water by in this case 30 degrees celsius so 30 times a thousand in this particular case this happens to be 30 000 calories that i needed to provide to raise a temperature of a thousand grams of water by 30 degrees celsius so this equation right here allows you to tie temperature differences two amount of energy needed to achieve that increase or decrease in temperature a very nice equation that we can use in something called calorimetry let's say that you want to measure how many calories are in a banana one way that you could do that is by using an instrument like this called a calorimeter a calorimeter has a chamber where you could place a banana and in this chamber there's oxygen and ignition wires so you could ignite the banana and it would start burning now surrounding this chamber there's water a specific amount of water right you build this you know exactly the mass of the water in here and then surrounding this water there are insulating walls so that heat cannot escape or come in all right so we insert the thermometer so that we can measure the temperature of the water and let's say before anything happens we measure the initial temperature of the water now and this could be stirring the water to disperse heat so let's say we ignite the banana let it burn your banana and let's say has carbon hydrogen oxygen and acid reacts with oxygen all the carbon reacts with oxygen to form carbon dioxide all the hydrogen reacts with oxygen to form water and of course it releases heat or calories and those are the calories that are contained in that banana so as this heat is being released it's heating the surrounding water so of course the temperature is going to start climbing once the banana is completely consumed and the temperature doesn't rise any longer we can record the final temperature so we've got the mass of the water we know since this is water that this that we're heating that the specific heat is one calorie per gram per degree celsius and we know the initial and final temperature of the water and so using this equation we can then calculate the number of calories that were contained in that banana because that's the number of calories that were used to heat this water by this number of degrees celsius so let's look at an example where we determine the number of calories in a certain fruit like half a vapor the information obtained from a calorimeter and using specific heat as a conversion factor to calculate calories so the problem says determine the caloric content for half a bagel given the following formation from a calorimeter expert experiment so the mass of water surrounding the ignition chamber is a thousand grams in the calorimeter we of course know the specific heat of water one calorie per gram per degree celsius uh before we ignite the half a bagel the initial temperature of the water is 22 degrees celsius after the bagel is completely consumed the final temperature of the surrounding water is 92 degrees celsius so we're going to use the equation that we just came up with where the number of calories released by the half a bagel equals the mass of the water in the calorimeter times the specific heat of the water because that is what is being heated times the temperature difference of the water what the initial temperature was before ignition what the temperature was after the half a bagel is completely gone and that's going to be 92 minus 22 degrees we'll make sure our units so that the only unit that is left here is calories 92 minus 22 is going to be 70 temperature difference times a thousand that's 70 000 calories which might seem a little bit excessive for half a bagel but it's actually not because these are not the calories that we're used to seeing printed on the back of food labels what we see on the back of food labels is something called a nutritional calorie one nutritional calorie with a capital c is actually equal to a thousand calories as we've defined in this lecture or equal to one kilo calorie this is a sort of american invention um given that in the u.s the metric system wasn't routinely used and so and they came up with this nutritional gallery in other places europe latin america you're going to see food labels either in kilocalories directly or perhaps in kilojoules all right so given that your 70 000 calories equals given this relationship 70 nutritional calories or 17 kilocalories so that answer certainly makes perfect sense for half a bagel so here is an example of a food label and the information that you find in here of course for this candy bar the number of calories of nutritional calories is 360. um these 360 calories are coming from every type of biomolecule in this candy bar if candy bar has carbohydrates proteins fats the sum total of the calories contained but each of these different food types adds up to 360 nutritional calories now we know that one gram of carbohydrate any type of carbohydrate if you put it in the calorimeter and you burn it we would calculate that one gram of carbohydrate contains or releases four kilocalories of energy for nutritional calories one gram of protein will release the same number of kilocalories in calorimeter one gram of fat releases almost more than double that amount nine kilocalories of energy this is why the long-term storage of energy in your body is in the form of fat because per gram it's towards the most amount of energy if i were storing long term my energy in the form of carbohydrates i'd have more than twice the mass to be able to store the same amount of energy and i really really don't need more than twice the mass that i already have so fat is the most efficient way of storing energy so we just learned that one gram of protein contains four kilocalories of energy and that is the same as one gram of carbohydrate and then one gram of fat equals nine kilocalories this is of course a conversion factor in other words if i know that for example one cup of milk 4 percent has 9 grams of fat then i can use this conversion factor to convert the grams of fat into kilocalories of energy and then i could consider the nine grams of protein and use this conversion factor to calculate the kilocalories in those nitrous protein and the same with the 12 grams of carbohydrate using this conversion factor so let's look at that problem all right we've got a cup of whole milk 12 grams of carbohydrate each gram of carbohydrate is four kilocalories and so 12 times four gives me 48 kilocalories from the carbohydrate of course as usual make sure that your units cancel out and that is the correct answer then we're looking at having nine grams of fat and each gram of fat it's nine kilocalories so nine times one is 81 calories and finally we have nine grams of protein each gram of protein calories so 9 times 4 is 36 foot calories all right now i add all my kilocalories and the entire cup of whole milk then has 165 kilograms all right which is exactly what they calculated here and you have a whole bunch of other problems you could do and make sure that you get the correct answer