 So, the next property we will be going to talk about is heat capacity, heat capacity as a name suggests it tries to quantify how much heat an object can store, it is a capacity of storing heat by an object, can one of you sit there, you can sit there, no no, so it should quantify how much heat an object can store, like for example, if I give you a bucket, if I give you a bucket like this, it is a huge bucket you cannot measure its dimensions for example, and you need to estimate what is the, let us say capacity of this bucket, all you have is 1 liter water, then what you should do, pour it that is all you can do right now, pour it and you will see that the height is more here and less here, fine, so with respect to how much water level is, you can estimate the capacity, you can say that capacity of this bucket is more, fine, so it is like whatever amount of liquid you are giving inside the bucket divided by whatever is the height, this height should give you an indication of what is the capacity of the bucket, lesser the height more is the capacity, fine, so I am just giving you a very good example of how you should understand the heat capacity, fine, so just like capacity to store water, similarly we are talking about capacity to store heat, when you give heat to an object, what will increase, temperature will increase, height will not any, height is for water, if you give heat to the substance is temperature will increase, so similarly if I take a measure of how much temperature has increased for a given amount of heat and giving it, I can call this as heat capacity, this is heat capacity which can be generated by a liter C, how many objects you have in this room, more than 100, if you just open that CPU, more than 100 will come out from that CPU itself, similarly you will see more than 100 objects in this classroom itself, imagine how many objects are there in the world, you cannot count, they are countless and then you cannot use this term heat capacity and go on listing down all the heat capacities of each and every object in the world, it become very tedious process, but then if you know heat capacity, if you know C for an object, if you know heat capacity for an object, how much heat it can absorb for let us say delta T rise, C into delta T, simply, so formula wise it is very simple, but practically listing down all the heat capacities for each and every object in this world is very difficult, so that is the reason why there has to be a simpler way to define heat capacity, so that I take into account of all the material in the earth, now ultimately any material you take, it is made up of elements, basic elements, how many elements you have in that periodic table, 108 or 109 like that, so can I safely say that entire earth is made up of those 108 or 109 elements, and out of those 108 and 109, there are just 6 or 7 of them which constitute more than 90 percent, fine, so if I define some capacity related thing for only those material which are like purest form, then all the objects are made up of those material only, getting it, for example this chair, it is made up of let us say wood, then iron, then cushion, cloth and everything is there, so if I know separately that for iron this is the capacity for wood, this is the capacity for cloth, for this cloth, this is, then I can you know individually cater to, like for example for iron I can find out how much heat it can absorb, for wood I can take it separately, once I split it, whatever object it is, if I split into its basic constituents, then it become very easy to handle, but problem lies here, that for example if I take 1 kg of iron, if it can absorb let us say 10 joules of heat and it can create only 1 degree Celsius rise, now if I take 2 kg of iron, then if it absorb 10 joules of heat, how much rising temperature will be, approximately half, half mass is double, we are getting it, so even though you are considering the material in its theorist form, but then also heat capacity is different for different masses, so it is a good idea to define heat capacity as per unit mass, per kg what is the heat capacity, so that is the reason why there is this term just called specific heat capacity, which is heat capacity per kg, so write down specific heat capacity, specific heat capacity is amount of heat absorbed by 1 kg of substance, it is the amount of heat absorbed by 1 kg of 1 kg of substance to increase the temperature by 1 degree Celsius, should be equal to what, delta q divided by m into delta q, now delta q will be equal to m s delta t by definition itself, now this specific heat is different for different material, for iron it is something, for steel it is something else, for copper it is something else like that, getting it, so if temperature is increased, heat will be absorbed, if temperature is decreased, same heat will be released, so if you already know that the decrease in temperature is like release of heat and increase of temperature is absorption of heat, you do not care about the sign coming in, you always subtract lower temperature from higher temperature, you take the modulus of it, let us suppose changing temperature is 5 degrees Celsius, whether it is increased or decreased, the quantum of heat is same, whether it is released or absorbed, so that is how you deal with and then you find out the heat involved in the process m s delta t, any doubt here, no, I think this concept was introduced in class 10, 9, in chemistry, m c and cv delta t, that is molar specific heat, yeah 9, now this specific heat capacity is a very good physical parameter for liquids and for solids, for gases the situation becomes little tricky, the problem is this, let me give you an example, suppose you are cooking a food inside a pressure cooker and suppose you are cooking food in an open utensil, where the food will be cooked faster, pressure cooker why, because temperature increases faster inside the pressure cooker, same gas is there, same gas at most it gas only is there, but it is able to increase its temperature more, if it is inside the pressure cooker with the same amount of heat, what is so special in the pressure cooker, the volume is constant, when it is open utensil, what is constant, pressure is constant, okay, so for gases we need to also take into account that whether it is a constant volume or constant pressure process, okay, constant volume specific heat is different, constant pressure it is different, okay, you learn more about it in thermodynamics, what happens is that the some amount of heat which gas absorbs goes into expansion, when you are allowing it to expand, okay, but when you are enclosing it, it cannot do any work, whatever heat you give, entire heat gets converted into rising temperature of that gas, fine, so that is the reason why same amount of heat when you give in constant volume the rising temperature is more, so now tell me where the specific heat capacity will be more in constant volume or in constant pressure, same amount of heat, let us say I am giving delta Q, delta Q, at constant volume delta T will be more, at constant pressure delta T is less, so delta Q by delta T is more in constant pressure, so at constant pressure specific heat of gas is more, okay and when we talk about gases generally we like to deal in moles, okay, that is why the heat capacity is not defined per kg of a gas but per mole of a gas, okay and we call it molar specific heat capacity, if you call it specific heat capacity it is still per kg only, you have to specify it is molar specific heat capacity, okay, so what should be the formula, at constant volume molar specific heat is written as Cv, which is equal to delta Q divided by what N into delta T, N is number of moles, okay, this is Cv heat is supplied at constant volume, okay, Cp is delta QT divided by N into delta T, okay, so if I give let us say 1 joule here, delta Q is 1 joule, here also 1 joule, which delta T will be more, this is constant volume delta T will be more, this is pressure vocalized scenario, right, delta T is more, temperature rises faster, so denominator is more than this denominator, that is why this is lesser than that, Cp is more than Cp, calorie metric, calorie is what, a unit of heat energy in a way, metric is measurement, it is like measuring something, okay, so measurement of heat is, calorie metric is a process of measuring the heat, okay, so in the calorie metric we will learn about an experiment to measure the heat itself, or this experiment will help you calculate the specific heat of particular substance, okay, have you ever heard of calorie metric down before, you are in CBS or ICS, do you see, see calorie metric uses a bucket sort of thing that is called calorie meter, okay, so you have this calorie meter, it is made up of an insulating material, you may want to put the foam inside or make it a wood, okay, you are doing it so that there is no exchange of heat from the surrounding, whatever happens inside remains inside, okay, then you have to put a lid also at the top, let's say it has water in it, now you are going to measure heat, so what is the first instrument you should have, thermometer, right, there is a thermometer which goes like this, okay, this is thermometer, okay, you may want to open the lid and then drop a very hot iron ball inside, so that heat is getting exchanged between iron ball and water and based on that you draw some inferences, okay, but when you do it, when it goes down, maybe water, this side is hotter, that side water is colder, temperature is not uniform, then what you should need, sterile, okay, so you have a sterile also, it will just mix everything, fine, so this is the calorie meter inside which you have exchange of heat which is happening and the best part is there is no exchange of heat from the surrounding, that is assumption actually, there will be some exchange of heat anyways, okay, but then what will happen inside the calorie meter, there will be some hot objects, right down, there will be hot objects before mixing and talking, like for example this is a hot iron ball, okay, there will be hot objects and then there will be cold objects, of course hot and cold, they are relative term, so I am saying the temperature difference is there, okay, so now when they are coming in contact and you have a sterile also, what will happen, exchange of heat, hot objects, what they will do, they will lose heat, they will lose heat energy and what the cold objects will do, they will gain heat energy, now is the magnitude of loss in heat energy is equal to the magnitude of gain in heat energy, yes or no, it will be, right, this is how you, this is nothing but consumption of energy only, this is how you use calorie meter to measure the heat, you are just equating the amount of heat that is lost by the hot object with the amount of heat that is absorbed by the colder object, now when you leave it like this, when the hot object comes in contact with the colder object and you with the stirrer do all that and leave it for very long time, what will happen, temperature becomes constant both for hot as well as cold, both will come at the same temperature, initially they may be having different temperature but finally they will come at the same temperature, okay, it may happen that in a numerical it is given like for example X amount of heat is given out to the atmosphere, then I think you are intelligent enough to equate, right, you can say that whatever heat hot object is releasing, that is equal to gain in heat energy by the colder object plus loss to the atmosphere, right, but majority of time they will not gain in loss to the atmosphere, okay, so all you have to do in numerical related to calorie meter is equate loss in heat energy with gain in heat energy, who will lose the heat energy, hot object and who will gain the heat energy, colder objects, very simple, okay, shall we do a numerical, delivered for delta Q is what, MS delta T, fine, till now our assumption is we are not changing state, it will never happen that right now I can, you know I can put an ice also, its state will change, it will become liquid, right, I am not touching that scenario right now, I am just talking about scenario where the states remains same, if initial state is liquid, the remain liquid, if initial state remains solid, now tell me one thing, there will be hot object, there will be colder objects, calorie meter is this bucket, let us say, okay, which will have a copper coating inside, will this calorie meter also absorb heat or release heat, current does, it can do, it can right, so you need to take into account the calorie meter also, fine, so initial temperature of calorie meter will be the temperature of all the objects inside the calorie meter initially, and the final temperature of calorie meter will be the final temperature of everything, which will be constant for all, getting it, okay, at times it will be given that calorie meter's water equivalent is 100 gram, what does it mean, it means that calorie meter will absorb same amount of heat as if 100 gram of water would have absorbed, fine, understood, so all these final nuances will be there in problem solving, may not be at your school level, but when you solve J level question, there will be such nuances, okay, let us take up a numerical number, a sphere of aluminum 0.047 kg is placed for sufficient time in a boiling water, so that the sphere's temperature becomes 100 degrees Celsius, so just write this one, a sphere of point, aluminum sphere of 0.047 kg is at 100 degrees Celsius initially, okay, it is immediately transferred to 0.14 kg copper calorie meter, so you have 0.14 kg of copper calorie meter inside which you are transferring this sphere, okay, the calorie meter already has 0.25 kg of water, it already has 0.25 kg of water at 20 degrees Celsius, fine, the temperature of the water rises and the final temperature becomes 23 degrees Celsius, fine, here you have to find out specific heat of aluminum, how much it is, specific heat of aluminum is what, what is given is specific heat of copper which is 0.386 into 10 square 3 joules per kg per degree Celsius, okay, what is specific heat of water, how much it is, you remember 4.18 or 4.2 whatever, 4.18 into 10 square 3 joule per kg per degree Celsius, who is losing heat, aluminum and who is gaining copper and water, just substitute the values over there, lost by the aluminum, m which is 0.047 into specific heat of aluminum into, data is what for aluminum, 100 to 23 it drops, so 77, this into 77, this is the heat loss by the aluminum, okay, this should be equal to heat gained by the copper, how much, mass of copper is 0.14, okay, specific heat of copper and 386 10 square 3 into delta T of copper is hot, 3 from 20 it goes to 23, 0.24, now water is also into 4.18 into 10 square 3 into 3, you will tell this only all of you, how much you are getting, approximately also this, when you solve it properly, you will get specific heat of aluminum to be equal to 911 joule per kg, calculation, calculation there is, but you should know which side you approximated, whether you have approximated to get less than the actual answer or more than the actual answer, you getting it what I am trying to say, approximation is fine, but you should know which side you are in, don't try to correct your calculations, you have to do it again, you have to do it right the first time, if you make a mistake, it becomes very difficult to identify it, okay, I will quickly discuss the next property as in I will just introduce it, I will not get into too much of details of it, because time is not permitting, the next property that we are going to take up is change of states, so you have suppose you have three states right solid, although there are actually two or three more states, but we are not getting into all that, we are talking about the usual three states, three states of matter, so solid can become liquid if you provide heat, this process is called what, what is this process, melting, this is called melting, technically this is also called fusion, okay, then this is what vaporization, okay, this heat, this is heat required to fuse the solid, okay, this is the heat required to vaporize, so let's say this is delta Q F, this is delta Q V less, okay, now when vapor becomes liquid, this is what absorption of heat, this much heat will be absorbed, but when vapor is becoming liquid, same amount of heat will be released, getting it, and similarly when liquid is becoming solid delta Q F will be fine, and also there is process where solid directly becomes vapor that is sublimation, okay, but we are not getting into all that right, okay, these are the process when vapor becomes liquid, this process is called what, condensation, when liquid is becoming solid, this is solidification, fine, now one unique thing about the transition is that when transition happens, temperature is constant, what is temperature, a measure of the kind energy of the molecules, okay, so when you get the heat and the state changes happening, kind energy doesn't change, then what is changing, potential energy, potential energy, and what is potential energy, energy purges because of the position, so the molecules are going further away from each other, so the potential energy is increasing, so whatever heat you are giving it, it is increasing the potential energy, kind energy is not increasing in the state change, getting it, so it's a constant temperature process during the transition, fine, and in case of water and in case of pressure is one atmosphere, this transition happens at 0 degree Celsius and that transition happens at 100 degree Celsius, fine, so transition temperature depends on the pressure as well as what is the material, but temperature will remain constant at a particular pressure, any doubts, no, so the heat that is required to melt this solid completely should depend on what, should depend on how much is the solid, how much, how many kgs, right, and should it depend on nature, temperature is anyway not changing, are you getting it, so when it is melting, when it is melting, delta Q is just mass into a constant which is latent heat of fusion, same formula holds good when liquid is becoming solid, solidification also, but this time when liquid becomes solid, it will release the same amount of heat, getting it, now one unique thing here, this is what, what is this, mass of what, this is not a total mass, this is the mass which has changed the state, out of 5 kg i's you just melted 1 kg, so this is 1 kg only, fine, when you write delta Q is equal to delta T, you are taking entire mass, but when you are writing M into LF, you are taking only that mass which is changing the state, remember that, this is melting or solidification both, and this is a huge amount of energy, latent heat of fusion is usually a very, very big number, and you see that, let me first introduce vaporization also, for vaporization or condensation, the amount of heat is mass of this liquid that is vaporizing into latent heat of vaporization, now have you ever seen like how your mom used to make sure that milk is, the hot milk is cool down very quickly, how it happens, what she does, you put it below the fan, have you ever seen that, right, so when you put it below the fan and fan is rotating, lot of vaporization happens, the vapor comes out from the milk, now during the vaporizing it needs that much heat, so from where it will take the heat, from the remaining milk, whatever is vaporizing it will take the heat from the remaining milk and go away, and vaporize, so the remaining milk is getting cooled down faster and faster, because vaporizing is happening, same thing happens when the sweat and wind is blowing, then our sweat is vaporizing, when sweat is vaporizing the heat which is required for it to vaporize it will take from our body, so we feel cold, that is the whole reason why human sweat, when there is a hot conditions, so that you feel cold, because vaporization should happen from this side, so next class we will take it more qualitatively and we will solve a lot of numerical on it, try to finish this chapter, and it helps, nothing.