Heat Capacity and Specific Heat

hello bobcats in this video we will be discussing heat capacity and specific heat so let&#39;s look at heat capacity first heat capacity which is represented with the capital c is the heat required to raise the temperature of a quantity of substance by one degree celsius or you can say one kelvin okay so um and so it&#39;s um the units for heat capacity are since it&#39;s the heat required units are joules per degree celsius or joules per kelvin now it you don&#39;t have to do any conversion between this well you do have to do conversion no you don&#39;t you don&#39;t have to do conversions because if you think about it we&#39;re talking about a change in temperature so if i have zero degrees celsius and i change it to one degree celsius that&#39;s just one unit of change well the same thing here because remember zero is 273 kelvin and if i change it to one the same here that&#39;s going to be 274 kelvin that&#39;s still one unit of change so i can use either one it depends on which temperature scale i&#39;m using the other thing we need to know is that heat capacity is an extensive property and what i mean by that is that it depends on the amount of substance okay so let&#39;s think about that for a second if i have 100 ml of water and i have one thousand mils of water it takes more energy to change the temp the temperature by one degree in one 000 mils than it does 100 mils so the 1 000 mils has more heat capacity so let&#39;s look at this so let&#39;s say it takes from more energy to heat 1000 milliliters of water by one degree celsius than it does to heat 100 mils a week water 1 degrees celsius then it does to heat 100 mils so we would say that the 1000 mils has more heat capacity than the 100 ml of water okay so it&#39;s an extensive property it depends on the amount and the equation for heat capacity would be c is equal to heat absorbed divided by temperature change or change in temperature okay or you can think of it as remember that&#39;s joules per degree celsius okay now the next thing we&#39;re going to look at is called specific heat so specific heat where do i have my or also known as specific heat capacity but we usually just say specific heat so specific heat capacity which we represent with a lowercase c is the amount amount of heat required to raise temperature of one gram of one gram of substance by 1 degree celsius so or 1 kelvin so in this case i&#39;m changing one gram so it&#39;s the amount of energy to take and change just one gram by one degree celsius and this means that this specific heat is an intensive property which um what what i mean by that whoops intensive property is that it does not depend on the amount of substance okay so specific heat is an intensive property and what we&#39;re saying here is that every substance has a requires a different amount of heat to raise that substance by one gram of that substance by one degree celsius and um the units for uh specific heat so the units for specific heat are joules over grams times degrees celsius or you can think of it as joules over grams times kelvin and in some cases you can even think of it as calories over grams degree celsius okay so but the most common unit to use is this one right here joules over grams per degree celsius now the um another thing we&#39;re going to look at is that since this is an intensive property but we also have molar heat capacity and molar heat capacity is when we look at let me write it down give me a second molar heat capacity is the same as specific heat capacity but our amounts are different and in this case instead of grams we&#39;re going to look at moles so molar heat capacity is the amount of energy or amount of heat required to raise the temperature of one mole instead of one gram it&#39;s one mole so sometimes you have to use molar mass to convert between grams and moles but it&#39;s the amount of tim the amount of heat required to change the temperature of one mole of substance not one gram one mole of substance by one degree celsius so it is also an intensive property the only the other thing is that the units are just slightly different my units are joules over mole degrees celsius or joules over mole kelvin okay so but it&#39;s the same thing but we&#39;re going to spend most our time talking about specific heat and less time about molar heat capacity i just want you to be aware of that now the next thing is let&#39;s look at the uh we can use an equation to determine the amount of uh heat absorbed by chemical and physical process and that equation is as follows so let me find a different colored pen to use here so the amount of heat absorbed or released it could be released heat absorbed or released biochemical process or physical process is the amount of heat absorbed so that&#39;s what we&#39;re looking at the amount of heat absorbed or released by a chemical process can be determined by the following equation using q equals m c delta t so you need to know this equation okay so again the amount of heat absorbed which is q or released by a chemical or physical process can be determined by using mc delta t and so we need to make sure we understand each of these variables remember q is equal to heat and it&#39;s measured in joules we know that m is equal to mass measured in grams we&#39;ve got c is equal to specific heat and that has units of joules over gram degrees celsius and then you have change in temperature which um is in units of we&#39;re going to stay with celsius so change in temp in degree and so that&#39;s going to be in degrees celsius now just a reminder anytime you see change remember change in anything in this case change in temperature is the final temperature minus the initial temperature so let&#39;s look at a couple problems using this equation the first one would be let me get these pins out of the way let&#39;s calculate the specific heat of water if 83.68 joules of heat is required to [Music] raise the temperature of to raise the temperature of four grams of water by 5 degrees celsius okay so here we have q we have mass and we have the change in temperature so if i write the equation out we have q is equal to m c delta t and i have to isolate in this case i have to isolate for c so i&#39;m going to rearrange that so c is equal to q over m times delta change in temperature delta t so when i substitute my values in we&#39;ll have 83.6 joules divided by a mass of 4.000 grams i&#39;m doing this because i want an answer with four sig figs times the change in temperature which is 5.00 degrees celsius and when i do that when i calculate all this my specific heat comes out to be four point 0.184 joules over grams times degrees celsius now this is a value you have to memorize because this is the specific heat of water and that&#39;s the only one you have to memorize i will give you a table of all the other specific heats but the one for water you have to memorize so make sure you know this one star star star memorize that one and this is a specific heat of water [Music] now water has a very high specific heat and it&#39;s a good thing that it does because what specific heat to understand specific heat or interpret specific heat um we need to think of well let me say this um substances with higher specific heat um resist temperature changes more than substance with low specific heat so let&#39;s write that down where&#39;s my paper i need a clean sheet of paper i&#39;ve got too much paper over here so substances with higher higher specific heat values resist temperature change more than substance with low specific heat values now water has one of the highest specific heats heat values and that&#39;s a good thing because that means it can absorb a lot more energy before it changes temperature so that&#39;s why the earth is at a constant of a relatively constant temperature i know there&#39;s a change like in you know if when it&#39;s really cold it can be a negative 30 and it&#39;s really hot 100 but that&#39;s not a big change for a planet so and the reason that the temperature on earth is so constant is because all of that heat energy from the sun that is um being absorbed by the water doesn&#39;t the water doesn&#39;t change temperature very much uh for example if i when you go to the beach and uh sand which is just basically silicon dioxide sand has a specific heat of one one degree one joule per gram degree celsius and so on a day when the sun is uh the the sand and the water is absorbing the same amount of energy from the sun the sand changes temperature and gets really hot because it has a low specific heat and the water didn&#39;t change very much it stays cool because it can absorb all that energy and not change temperature so let&#39;s just look at a couple examples of this so here&#39;s some specific heats of specific um a couple examples of substances so specific heat examples so again um that my blue is just about to run out so i&#39;ve got to change colors here so um water remember water as a liquid h2o as a liquid is 4.8 now remember this is in joules over grams degrees celsius so 4.184 joules per gram degrees celsius we also have to look at the state&#39;s matter so water as a solid would be 2.089 and water as a gas is even a little bit lower 2.042 now these are pretty high because if you think about it uh the next one that is close to this would be let&#39;s look at let&#39;s say [Music] look at nitrogen gas because that&#39;s our atmosphere right so nitrogen gas has a specific heat value of 1.04 and then if we look at some of the metals let&#39;s look at aluminum aluminum put an equal sign is equal to 0.892 [Music] so it has a much lower specific heat value so if i were to um give an aluminum a block of aluminum the same amount of energy that i would give water the aluminum would would increase in temperature much more so aluminum will have a much greater temperature change with the same amount of heat than water would so there&#39;s aluminum something let&#39;s look at something that&#39;s familiar let&#39;s talk about gold man gold is really low it&#39;s at 0.129 [Music] so that&#39;s much lower and then let&#39;s just do one more very familiar one let&#39;s look at iron iron has a 0.442 so metals have very low specific heats and that means that when you give when you apply any kind of heat to them they will change temperature very quickly and with a great deal of change whereas water doesn&#39;t change much at all i mean think about this water is how many more times uh that of gold so the specific heat of water is 30 times uh and is 30 times greater than that of gold so it won&#39;t change very much compared to what gold will and it&#39;s because of the low specific heat values of metals is why they also conduct heat very well now the last thing we&#39;re going to do is just do one more practice problem with specific heat and then i&#39;ll be done with this video and so the last practice problem let me find where i put it i think i left it somewhere hang on sorry about that okay so in this case we&#39;re into uh examples so let&#39;s do another example calculate the final temperature the final temperature after 1485 joules of energy or heat is added to 16.7 grams of water starting at 23.4 degrees celsius okay so i&#39;m going to write my variables uh it&#39;s the best thing to do so we don&#39;t get we don&#39;t lose track we know that this value right here that&#39;s q so q is equal to 1485 joules i also need to make sure all my units match and then this is mass so we have mass is equal to 16.7 grams of water so it&#39;s not given here but remember i said you had to memorize so the specific heat of water is 4.184 joules over grams degrees celsius and then starting at 23.4 degrees so that&#39;s a an initial temperature of 23.4 degrees celsius so we&#39;re looking for the final temperature we don&#39;t know what that is now the equation that we&#39;re going to use remember is q is equal to m c delta t now delta t don&#39;t forget remember delta t is equal to t final minus t initial so if i can find delta t then i can use it to substitute here because i already have uh initial temperature so let&#39;s isolate this equation for delta t so i want to isolate for delta t here and so what i do is i divide both sides by m c so delta t is equal to [Music] q over m times c specific heat and i have these values so i&#39;m going to go 1485 joules over the mass which is 16. grams times my specific heat of water which is 4.184 joules over grams times degrees celsius now i&#39;m going to make sure my units all cancel out so when i do that there&#39;s a joule on top and a joule on the bottom so joules cancel then i have a grams on top and grams on bottom and i&#39;m left with a degree celsius but remember a denominator of a denominator is a numerator so my change in temperature is equal to 21.31 degrees celsius but that&#39;s not the answer remember we&#39;re going to use this equation right here so don&#39;t forget delta t is equal to t final minus t initial i need to isolate again for t final so that would be adding ti to both sides so t final is delta t plus t initial and so that&#39;s going to be 21.3 oops degrees celsius plus what we had over here to start 23.4 degrees celsius so my final temperature the answer is 44.7 degrees celsius that&#39;s the final temperature and so when you do a problem like this i would make sure you&#39;ve got all your variables uh identified and make sure all the units will match because sometimes you&#39;ve got kilograms sometimes you might even get a kilojoules or calories or celsius and kelvin you need to make sure all the units are going to work then you would write the equation here&#39;s my equation then substitute or rearrange the equation to isolate what you&#39;re looking for substitute and then if you&#39;re doing uh initial or final temperatures you find the delta t and then substitute into this this equation delta t is equal to final temperature minus initial temperature and that is the end of heat capacity and specific heat

hello bobcats in this video we will be discussing heat capacity and specific heat so let&amp;#39;s look at heat capacity first heat capacity which is represented with the capital c is the heat required to raise the temperature of a quantity of substance by one degree celsius or you can say one kelvin okay so um and so it&amp;#39;s um the units for heat capacity are since it&amp;#39;s the heat required units are joules per degree celsius or joules per kelvin now it you don&amp;#39;t have to do any conversion between this well you do have to do conversion no you don&amp;#39;t you don&amp;#39;t have to do conversions because if you think about it we&amp;#39;re talking about a change in temperature so if i have zero degrees celsius and i change it to one degree celsius that&amp;#39;s just one unit of change well the same thing here because remember zero is 273 kelvin and if i change it to one the same here that&amp;#39;s going to be 274 kelvin that&amp;#39;s still one unit of change so i can use either one it depends on which temperature scale i&amp;#39;m using the other thing we need to know is that heat capacity is an extensive property and what i mean by that is that it depends on the amount of substance okay so let&amp;#39;s think about that for a second if i have 100 ml of water and i have one thousand mils of water it takes more energy to change the temp the temperature by one degree in one 000 mils than it does 100 mils so the 1 000 mils has more heat capacity so let&amp;#39;s look at this so let&amp;#39;s say it takes from more energy to heat 1000 milliliters of water by one degree celsius than it does to heat 100 mils a week water 1 degrees celsius then it does to heat 100 mils so we would say that the 1000 mils has more heat capacity than the 100 ml of water okay so it&amp;#39;s an extensive property it depends on the amount and the equation for heat capacity would be c is equal to heat absorbed divided by temperature change or change in temperature okay or you can think of it as remember that&amp;#39;s joules per degree celsius okay now the next thing we&amp;#39;re going to look at is called specific heat so specific heat where do i have my or also known as specific heat capacity but we usually just say specific heat so specific heat capacity which we represent with a lowercase c is the amount amount of heat required to raise temperature of one gram of one gram of substance by 1 degree celsius so or 1 kelvin so in this case i&amp;#39;m changing one gram so it&amp;#39;s the amount of energy to take and change just one gram by one degree celsius and this means that this specific heat is an intensive property which um what what i mean by that whoops intensive property is that it does not depend on the amount of substance okay so specific heat is an intensive property and what we&amp;#39;re saying here is that every substance has a requires a different amount of heat to raise that substance by one gram of that substance by one degree celsius and um the units for uh specific heat so the units for specific heat are joules over grams times degrees celsius or you can think of it as joules over grams times kelvin and in some cases you can even think of it as calories over grams degree celsius okay so but the most common unit to use is this one right here joules over grams per degree celsius now the um another thing we&amp;#39;re going to look at is that since this is an intensive property but we also have molar heat capacity and molar heat capacity is when we look at let me write it down give me a second molar heat capacity is the same as specific heat capacity but our amounts are different and in this case instead of grams we&amp;#39;re going to look at moles so molar heat capacity is the amount of energy or amount of heat required to raise the temperature of one mole instead of one gram it&amp;#39;s one mole so sometimes you have to use molar mass to convert between grams and moles but it&amp;#39;s the amount of tim the amount of heat required to change the temperature of one mole of substance not one gram one mole of substance by one degree celsius so it is also an intensive property the only the other thing is that the units are just slightly different my units are joules over mole degrees celsius or joules over mole kelvin okay so but it&amp;#39;s the same thing but we&amp;#39;re going to spend most our time talking about specific heat and less time about molar heat capacity i just want you to be aware of that now the next thing is let&amp;#39;s look at the uh we can use an equation to determine the amount of uh heat absorbed by chemical and physical process and that equation is as follows so let me find a different colored pen to use here so the amount of heat absorbed or released it could be released heat absorbed or released biochemical process or physical process is the amount of heat absorbed so that&amp;#39;s what we&amp;#39;re looking at the amount of heat absorbed or released by a chemical process can be determined by the following equation using q equals m c delta t so you need to know this equation okay so again the amount of heat absorbed which is q or released by a chemical or physical process can be determined by using mc delta t and so we need to make sure we understand each of these variables remember q is equal to heat and it&amp;#39;s measured in joules we know that m is equal to mass measured in grams we&amp;#39;ve got c is equal to specific heat and that has units of joules over gram degrees celsius and then you have change in temperature which um is in units of we&amp;#39;re going to stay with celsius so change in temp in degree and so that&amp;#39;s going to be in degrees celsius now just a reminder anytime you see change remember change in anything in this case change in temperature is the final temperature minus the initial temperature so let&amp;#39;s look at a couple problems using this equation the first one would be let me get these pins out of the way let&amp;#39;s calculate the specific heat of water if 83.68 joules of heat is required to [Music] raise the temperature of to raise the temperature of four grams of water by 5 degrees celsius okay so here we have q we have mass and we have the change in temperature so if i write the equation out we have q is equal to m c delta t and i have to isolate in this case i have to isolate for c so i&amp;#39;m going to rearrange that so c is equal to q over m times delta change in temperature delta t so when i substitute my values in we&amp;#39;ll have 83.6 joules divided by a mass of 4.000 grams i&amp;#39;m doing this because i want an answer with four sig figs times the change in temperature which is 5.00 degrees celsius and when i do that when i calculate all this my specific heat comes out to be four point 0.184 joules over grams times degrees celsius now this is a value you have to memorize because this is the specific heat of water and that&amp;#39;s the only one you have to memorize i will give you a table of all the other specific heats but the one for water you have to memorize so make sure you know this one star star star memorize that one and this is a specific heat of water [Music] now water has a very high specific heat and it&amp;#39;s a good thing that it does because what specific heat to understand specific heat or interpret specific heat um we need to think of well let me say this um substances with higher specific heat um resist temperature changes more than substance with low specific heat so let&amp;#39;s write that down where&amp;#39;s my paper i need a clean sheet of paper i&amp;#39;ve got too much paper over here so substances with higher higher specific heat values resist temperature change more than substance with low specific heat values now water has one of the highest specific heats heat values and that&amp;#39;s a good thing because that means it can absorb a lot more energy before it changes temperature so that&amp;#39;s why the earth is at a constant of a relatively constant temperature i know there&amp;#39;s a change like in you know if when it&amp;#39;s really cold it can be a negative 30 and it&amp;#39;s really hot 100 but that&amp;#39;s not a big change for a planet so and the reason that the temperature on earth is so constant is because all of that heat energy from the sun that is um being absorbed by the water doesn&amp;#39;t the water doesn&amp;#39;t change temperature very much uh for example if i when you go to the beach and uh sand which is just basically silicon dioxide sand has a specific heat of one one degree one joule per gram degree celsius and so on a day when the sun is uh the the sand and the water is absorbing the same amount of energy from the sun the sand changes temperature and gets really hot because it has a low specific heat and the water didn&amp;#39;t change very much it stays cool because it can absorb all that energy and not change temperature so let&amp;#39;s just look at a couple examples of this so here&amp;#39;s some specific heats of specific um a couple examples of substances so specific heat examples so again um that my blue is just about to run out so i&amp;#39;ve got to change colors here so um water remember water as a liquid h2o as a liquid is 4.8 now remember this is in joules over grams degrees celsius so 4.184 joules per gram degrees celsius we also have to look at the state&amp;#39;s matter so water as a solid would be 2.089 and water as a gas is even a little bit lower 2.042 now these are pretty high because if you think about it uh the next one that is close to this would be let&amp;#39;s look at let&amp;#39;s say [Music] look at nitrogen gas because that&amp;#39;s our atmosphere right so nitrogen gas has a specific heat value of 1.04 and then if we look at some of the metals let&amp;#39;s look at aluminum aluminum put an equal sign is equal to 0.892 [Music] so it has a much lower specific heat value so if i were to um give an aluminum a block of aluminum the same amount of energy that i would give water the aluminum would would increase in temperature much more so aluminum will have a much greater temperature change with the same amount of heat than water would so there&amp;#39;s aluminum something let&amp;#39;s look at something that&amp;#39;s familiar let&amp;#39;s talk about gold man gold is really low it&amp;#39;s at 0.129 [Music] so that&amp;#39;s much lower and then let&amp;#39;s just do one more very familiar one let&amp;#39;s look at iron iron has a 0.442 so metals have very low specific heats and that means that when you give when you apply any kind of heat to them they will change temperature very quickly and with a great deal of change whereas water doesn&amp;#39;t change much at all i mean think about this water is how many more times uh that of gold so the specific heat of water is 30 times uh and is 30 times greater than that of gold so it won&amp;#39;t change very much compared to what gold will and it&amp;#39;s because of the low specific heat values of metals is why they also conduct heat very well now the last thing we&amp;#39;re going to do is just do one more practice problem with specific heat and then i&amp;#39;ll be done with this video and so the last practice problem let me find where i put it i think i left it somewhere hang on sorry about that okay so in this case we&amp;#39;re into uh examples so let&amp;#39;s do another example calculate the final temperature the final temperature after 1485 joules of energy or heat is added to 16.7 grams of water starting at 23.4 degrees celsius okay so i&amp;#39;m going to write my variables uh it&amp;#39;s the best thing to do so we don&amp;#39;t get we don&amp;#39;t lose track we know that this value right here that&amp;#39;s q so q is equal to 1485 joules i also need to make sure all my units match and then this is mass so we have mass is equal to 16.7 grams of water so it&amp;#39;s not given here but remember i said you had to memorize so the specific heat of water is 4.184 joules over grams degrees celsius and then starting at 23.4 degrees so that&amp;#39;s a an initial temperature of 23.4 degrees celsius so we&amp;#39;re looking for the final temperature we don&amp;#39;t know what that is now the equation that we&amp;#39;re going to use remember is q is equal to m c delta t now delta t don&amp;#39;t forget remember delta t is equal to t final minus t initial so if i can find delta t then i can use it to substitute here because i already have uh initial temperature so let&amp;#39;s isolate this equation for delta t so i want to isolate for delta t here and so what i do is i divide both sides by m c so delta t is equal to [Music] q over m times c specific heat and i have these values so i&amp;#39;m going to go 1485 joules over the mass which is 16. grams times my specific heat of water which is 4.184 joules over grams times degrees celsius now i&amp;#39;m going to make sure my units all cancel out so when i do that there&amp;#39;s a joule on top and a joule on the bottom so joules cancel then i have a grams on top and grams on bottom and i&amp;#39;m left with a degree celsius but remember a denominator of a denominator is a numerator so my change in temperature is equal to 21.31 degrees celsius but that&amp;#39;s not the answer remember we&amp;#39;re going to use this equation right here so don&amp;#39;t forget delta t is equal to t final minus t initial i need to isolate again for t final so that would be adding ti to both sides so t final is delta t plus t initial and so that&amp;#39;s going to be 21.3 oops degrees celsius plus what we had over here to start 23.4 degrees celsius so my final temperature the answer is 44.7 degrees celsius that&amp;#39;s the final temperature and so when you do a problem like this i would make sure you&amp;#39;ve got all your variables uh identified and make sure all the units will match because sometimes you&amp;#39;ve got kilograms sometimes you might even get a kilojoules or calories or celsius and kelvin you need to make sure all the units are going to work then you would write the equation here&amp;#39;s my equation then substitute or rearrange the equation to isolate what you&amp;#39;re looking for substitute and then if you&amp;#39;re doing uh initial or final temperatures you find the delta t and then substitute into this this equation delta t is equal to final temperature minus initial temperature and that is the end of heat capacity and specific heat

Transcript for:Heat Capacity and Specific Heat

Transcript for:
Heat Capacity and Specific Heat