 So today we are going to start this chapter Thermal Properties of Matter. So this is the first chapter of study of heat and its phenomenon, writing it. Now this is the entire section in physics where you study about thermal properties of matter, then you learn about how you convert heat energy into work in thermodynamics and then you get into the details of exactly how the velocity of the molecules can contribute to pressure or can contribute to energy okay. So you exactly get to know what are the micro factors what is happening because of which the temperature is increased for a particular you know substance. So all that will constitute inside a big chunk of your class 11 which is no thermodynamic, thermo-property of matter and kinetic theory of gases alright. So this constitutes in and around 10 to 15 percent of your you know let's say J syllabus as such okay. So a good number of questions come from this section alright and the best part is what? It's very easy okay and that's probably the another reason why a student take it for granted and they will be like okay I'll be doing it at the end. Let me do the difficult part first. What happens because of that is your difficult part never improves and you use out on the easy part also okay. So make sure you are very good at thermodynamics which is probably the easiest section of your class 11 fine. So be very attentive in class anywhere whenever you have doubt please feel free to ask okay. Make sure you are very very good at this entire section okay. This study of heat and its phenomena this has been done for ages now. In fact you know when people have started understanding about physics as a branch they have studied there they have studied first about the heavenly objects like stars, sun and all that. So astronomy was considered to be the oldest branch of science okay and later on when the fire was discovered and they they came to know something heat is one of the form of energy then the study of heat also picked up okay. The study of mechanics sorry study of the motion of object and then study of rigid body and all that came much later on okay. So thermodynamics is one of the oldest branch of science where we study the heat and its phenomena okay. The first chapter in that series right down is thermal properties. So you will see in your book number 2 you are essentially learning about properties of different things. First chapter is what mechanical properties of solids then what mechanical properties of fluids now thermal properties of matter. So we are not studying thermal properties of solids separately and thermal properties of liquids separately okay because with respect to thermal properties they are behaving in a similar way fine. So entire matters thermal property is what we are going to learn in this particular chapter okay. Now can you tell me first of all tell me what do we mean by property? Property means what like for example what's your name? Aditya like suppose if I talk about what are the properties of Aditya. So what will come in my mind as in something which is very specific to Aditya isn't it right? I will not say that Aditya is a student okay that's the generic thing. So when I say property of anything a specific thing will come in my mind alright. So now when I say thermal properties of matter thermal properties of matter. So what should come in my mind something which get affected by something related to heat or temperature? Look at it some properties that are related with heat and temperature can you tell me few properties which are related to heat and temperature for a particular substance pressure of a gas is related with the temperature okay what else? Volume does it depend on the temperature? Does it change? If I change the temperature does volume change? It changes right. So expansion expansion of an object is a thermal property okay that we are going to learn in this particular section okay. So write down property number one the first property this is what thermal property of matter. So we are just listing down what are those thermal properties okay. The first prime property is thermal expansion. So we will get into the details of it right now we are just focusing on what could be the properties that we should focus on okay. This is one of the properties any doubt here okay. It says that whenever you heat any object increase its temperature its volume will increase all right. What else can you think of anything else? This is the first property second one the temperature is the cause okay. Now see why this thermal expansion is a property? Because two different substances will expand differently for a given change in temperature okay. So it's a unique property expansion of one object is different from the other object for a given temperature change. So that is why it is a property. Had it been that all the object expand equally with the same amount of temperature change then it is not a property of a object. Now can you think of any other property other than thermal expansion? State now what do you mean by state? State of matter liquid gas or solid. Now is that a thermal property if I let's say heat up an object a solid object will it state change after some time depends but then it will eventually convert into liquid isn't it and then it will convert into vapor like what happens with water its ice and then it melts and then evaporates and that happens because you're giving it heat right. Now can you tell me is that a property of a substance can two substances they they require different amount of heat to change their states right. They require like for example if you heat an iron object it will require much more heat to melt than melting ice. So state change is second property. So what I mean by state change is solid converting into liquid and then converting into vapor. Different amount of heat is required to change the state from one state to the other state for different objects. So that is why it is a property. Now can you think of any other property think about I mean it's okay if you are wrong. What do you mean by heat capacity? Okay now suppose you have two objects if I give let's say same amount of heat to both the objects. Will the change in temperature be same? Should it be same for both the object? Not necessary right. Suppose you give let's say five joules of heat to a very good conductor of heat. Okay its temperature will immediately increase. Okay but if you give the same amount of heat to a bad conductor of heat it will not increase very fast. So there has to be some term defined which takes care of the fact as in how much heat is required to increase the temperature. So the best way to quantify this property is heat required per degree change in temperature which will be different for different objects. Yes or no? Right and that property heat required to change per degree temperature is heat capacity. Fine so the third property is heat capacity. This heat required divided by however much temperature as reason because of that. Different object will have different heat capacity. Okay we will come back to specific heat capacity later on right now we are just defining heat capacity that is more generic than specific heat capacity. Okay now can you think of fourth property now? Property number four what do you think? Energy is taken care by this. Latent heat is taken care by this. Latent heat is required to change the state that will be different for different options. Okay fourth property I just give you a hint. Suppose you are cooking food in a copper utensil or suppose you are cooking food in stainless steel where the food will be cooked faster. Copper one. How fast heat is conducted from one point to the other point? Is that a property? That is a property right? For example if there is some hot object if you try to touch it through an iron rod the heat will conduct to you at a much faster rate than if you just poke it with a bad conductor of heat. So how fast heat is getting conducted? That itself is a property of a substance. Okay so the fourth property is heat transfer which is nothing but rate of transfer of heat energy. Okay any doubts? These are the four properties that we are going to learn in this chapter one by one. Okay so we will take property number one initially. Okay but before getting into property we need to first understand what is temperature right and what is heat and how they are different from each other. Can you tell me what is temperature? What it is? What do you mean by that? No but heat can also be specified right? Heat is energy so it can be written in the form of joules. Heat is a flow of energy. Heat flows or heat goes heat energy goes from one object to the other object. Okay just like water flows from one point to the other point. Why water flows from one point to other point? Because of the pressure difference right because the pressure difference water flows and because of temperature difference heat flows. Okay so you can drop parallel with let's say flutes and try to understand it. Okay and if you go to the micro level as in what it is exactly. Okay suppose gas molecules are there in this room. Okay I am talking about what is heat I mean what happens to the gas molecule if the temperature increases. If the temperature increases the kinetic energy of gas molecule increases. Okay so what happens is that when a gas molecule hit your hand then it will transfer its little bit of kinetic energy into your hand. Okay and you'll feel the heat. Okay so if there's lot of transfer of energy from the gas molecule on your hands you'll feel you'll feel that more amount of heat is there. Okay now temperature is a measure of indirectly to the measure of how much is the kinetic energy in the gas. Right more is the kinetic energy in the gas more it can transfer. Okay so temperature in a way is a measure of kinetic energy of the gas molecules. Okay now what is pressure? Pressure also happens because of gas molecules. What is that? When the force gets accepted when the gas molecule collide. Okay they will not only transfer the energy they will transfer the momentum also. Fine that transfer of momentum creates the force rate of change of momentum creates the force and that creates the pressure and the transfer of energy creates the flow of heat. Okay now the problem is that we cannot go about looking at the gas molecule and then try to say that okay temperature is I mean rather than temperature you best way was that you just find all the kinetic energy of the molecules all of it and then say that okay just forget about temperature this is the kinetic energy but it becomes a very tedious process and inaccurate process. Fine so there is this term called temperature which is defined which tells you you know relatively what is the kinetic energy of the molecules. So this is what the temperature is and there has been there had been lot of research as in in past to just quantify what it is because during those days people were trying to quantify each and everything defined like for example length length was quantified okay this much is one meter this much is probably one feet like that they have quantified okay and similarly they have quantified mass time and everything they have quantified but when it comes to something like temperature they were not able to quantify it very well. The reason is that when I say zero length what it is what does it mean zero meters means nothing is there less than zero length is not possible get it simply less than zero kg is not possible so there is absolute zero there you cannot go below that right similarly you need to define the temperature in such a way that zero means zero are you getting it but nobody was able to find during that time what is zero what is absolute zero fine so that is the reason why they could not identify an absolute scale so they took the help of the most common thing available to everyone which is what water okay and with respect to water they have come up with a scale to measure the temperature understand right so but then when they have defined they will assume something to be zero they will say okay fine where the water freezes at zero degree Celsius but is less than zero possible yes it is possible so that zero is not absolute zero getting it that's just a relative zero it is zero with respect to the water at that level getting it so degree Celsius scale is defined right now this temperature scale is defined see what happens is when you know that absolute scale for example for length we know zero is zero so all you to do is define what is one meter then two meters double of that three meters triple of that like that it becomes straight forward thing but when it comes to relative scale you need to first assume what is zero and then you have to assume what is one get it so the assumption here is that write down the temperature of ice temperature of ice is assumed to be zero degree Celsius just like you assume gravitation potentiality to be zero at some horizontal level even though it is not getting it like that we are assuming something to be zero degree which is temperature of ice okay and then we are assuming temperature of boiling water to be 100 degree Celsius all this is happening at one atmosphere fine okay and between ice and this boiling point entire scale is divided into 100 equal parts okay so it's a linear scale fine equally spaced intervals from 0 to 100 any doubts now if I have defined a scale like this can you get an idea of what is 150 if you just move one one step whatever you have defined you know exactly what is one right so after 100 you just add 50 of 1s look at 150 right so that's how Celsius scale is defined okay and then during the same time in England there was this Fahrenheit scale that was developed degree Fahrenheit I call it Fahrenheit scale here they have taken some other basis they haven't taken water I'm not actually very sure what basis they have taken but you know and they have taken the basis in such a way that the temperature of melting ice and this is melting ice okay melting ice because ice can be at less than 0 degree Celsius also but melting ice has to be at zero okay so temperature of melting ice is 32 degree Fahrenheit boiling water any idea what it is 212 degree Fahrenheit any doubts and now both are linear scale as in between 32 and 212 what is the difference 212 and 32 180 right so 180 equal divisions are there here 100 equal divisions are there okay now if I tell you a temperature in degree Celsius can you convert into Fahrenheit or vice versa can you do that try to see whether you can derive it assume that temperature in degree Celsius scale is C what is F anyone how will you go about it any idea tell me this if I plot this graph suppose on y axis you have Fahrenheit and on x axis you have degrees Celsius okay will it be a straight line it may be a straight line it has to be both are linear scales okay both are linear scale so there will be a straight line equation between F and C okay can you find out the line okay can you plot a line do that you have two points right yeah yeah that's the way you have to do it since it is a straight line the slope should be same what is the first point when degree Celsius is 0 Fahrenheit is 32 so this is the first point 0 comma 32 okay second point 212 comma 100 comma 212 so this point is 100 comma 212 fine you have this as your straight line fine now since it is a straight line the slope should be constant right so you just assume a random point somewhere here whose coordinates are C comma F okay take these two points initially and then these two points equate the slope from 2 point so if you take A and C the slope should be 212 minus 32 divided by 100 minus 0 this should be equal to F minus 32 divided by C minus 0 and out so we have F minus 32 divided by 180 is equal to C by 100 okay C is equal to 5 by 9 F minus 30 right so this is how you can derive a relation between degree Celsius and Fahrenheit any doubts so if I give you a temperature in degree Celsius you should be able to convert in degree Celsius now people didn't stop there they were always trying to find out is there any absolute scale okay so in that particular quest there was one experiment that was conducted with gases okay so let's see what is that experiment this is the temperature and this one is the pressure now they have taken a gas at a particular pressure in temperature so this is the initial pressure in temperature okay now they are cooling it down what will happen to its temperature down pressure down okay so next point is observed okay then again they are cooling it down another point is also like that when they are connecting it they are getting like this a straight line and after this point the gas liquefies it changes the state fine but if you extend the line you know that pressure cannot be less than 0 okay so when pressure is 0 they are trying to find what could have been the temperature so this gas liquefied because it's a real gas it's not an ideal gas had it been the ideal gas it will not liquefy and it will just come and hit here and this temperature is minus of 273.15 degrees Celsius okay now this is for only one gas let's say gas 1 okay similarly they have taken another gas alright now they when they have taken another gas they are also they are trying to liquefy it as in sorry they are trying to decrease the temperature which temperature decreased and then to their surprise it came and meet the same point when pressure is 0 the temperature of both the gases appear to be at same point okay no matter which gas you take approximately all the gases they are converging at the same temperature as if there is something unique for that temperature something unique about this temperature okay what is that unique thing temperature cannot go below this because negative pressure is not defined it's not possible fine so if temperature cannot go below this what does it mean this is the absolute temperature this is the absolute 0 okay so there comes a new scale which is an absolute scale so since it is an absolute scale we don't call it degree degree is a relative term like degrees Celsius degree Fahrenheit it's a relative comparison with some substance Kelvin is not a comparison it's an absolute scale okay so Kelvin scale is defined right down Kelvin temperature scale is defined in such a way that 0 Kelvin is actually minus of 273.15 degree Celsius sorry yeah 0 Kelvin is this and change in temperature in Kelvin delta as in 1 Kelvin is change of 1 Kelvin is equal to change of 1 degree Celsius getting it so delta t in Kelvin is equal to delta t in degree Celsius they are equal fine so you will see lot of formulas in this chapter where delta t will come okay so you don't need to convert degree Celsius into Kelvin or Kelvin to degree Celsius because both delta t's are same okay but if suppose there is a formula in which only t is coming like sigma e 80 is power 4 there is no delta t there you need to convert temperature into Kelvin which is an absolute scale okay this happens to the to be the SI unit also for temperature Kelvin okay any doubts no now can you tell me if a temperature is C degree Celsius or let's say x degree Celsius what is its temperature in Kelvin how much that should be x plus 273.15 okay so this much temperature in degree Celsius is equivalent to x plus 273.15 okay and just so that our calculation is simpler we many times ignore 0.15 we just say 273 we just add 273 degree Celsius to arrive at the SI unit of the temperature which is Kelvin fine any doubt with introduction to temperature right so this is how we measure the temperature once you know how you can measure the temperature now you can talk about the thermal properties one by one okay now like what we have discussed you know you can devise your own way of measuring temperature you can have a gas trapped inside container and you can define in such a way temperature that pressure when the temperature pressure when ice is melting and that temperature you know that pressure corresponds to some temperature and that boiling water what is the pressure inside that container correspond to some other temperature you can develop and scale yourself getting my point okay so don't feel I mean afraid of solving such questions because if you go and solve some high level questions they will you know twist the question in such a way that you know you get I mean many times you assume that okay fine this is Kelvin scale this is degree Celsius scale this is Fahrenheit scale and that's it but what happens is that a good question will test you on the basics whether you have understood how the scales are defined they will give a scenario in such a way that they'll say okay assume there is a new temperature scale that has developed so this is our condition so you need to be very good at analyzing the situation but then that will come through problem practice we'll do it a little bit later right now our focus is property number one which is thermal expansion right now this is a property of every substance and it says that the substance write down the substance will expand okay substance will expand if the temperature of the substance is increased the temperature of the substance is increased what will happen to a substance if the temperature is decreased your contract okay so whatever was the situation before we will come back to that fine so this is what we are going to learn now when I say expand expansion what do you mean by that expansion is expansion of length expansion of width expansion of area or expansion of volume what do you mean expansion of volume expansion of everything all the dimensions each and every dimension will expand fine with length width area or volume everything will expand okay so we will talk about it one by one first we'll take the most simplistic scenario that is linear expansion right now linear expansion and in a way you know area is nothing but multiplication of two linear dimensions so if linear expansion is there volume expansion is anyway there and if a real expansion is there volume anyway is there okay so they are interlinked linear expansion have you learned a little bit about calculus little bit like for example something is varying curve sort of thing then you assume a very very small interval and then you say that in that small interval you can assume it to be linear even though it is a curve okay similarly here the expansion is so less expansion is so less that you can assume that it changes linearly with the temperature what I mean to say is that if you consider length you consider length L if this length changes by delta L for delta T increase in temperature if you change the temperature by 2 delta T how much will be an increase in length 2 delta L 2 delta L okay so you assume it to be sequential increase or linear increase with the temperature fine now let's get into little bit more detail suppose I take a rod let's say a rod has length L okay you have provided heat to the rod and its temperature has changed from T naught from T naught its temperature has gone to T naught plus delta T T naught plus delta T so increase in temperature is delta T and length is increased to L plus delta L okay now can you tell me this delta L increase in the length should be proportional to what delta T immunity that will come in on my delta T it should be proportional to delta T what else delta L should be proportional to what else it should be like it should depend on delta T delta L should depend on material of course because it is a property of a material it has to depend on what is a material otherwise it is not a property of substance okay what else that does it depend on L also delta L if I take half the length L by 2 will delta L be still the same or it will be different if I just take L by 2 length L by 2 okay I divide this rod into L by 2 and L by 2 okay if I increase the temperature what should be the expansion here if delta L was initial it should be delta L by 2 here and delta L by 2 there are you getting it or let me give you a you know a simple way to visualize you take a rubber band and you stretch it if shorter the rubber band same amount of force small extension is there longer the rubber band same amount of force longer the extension okay each and every part will expand this L by 2 will expand now so each and every part here will expand but the total length is L by 2 right now so total expansion to delta L by 2 so in a way the expansion depends on the original length also fine so delta L is proportional to whatever was the initial length let's call it as L now fine now these are the two mathematical relations okay so I can combine these two and I can say that delta L is proportional to L0 into delta t I can say that okay now I will put a proportionality constant okay I will put a proportionality constant and I will say that that propositive constant is specific to the material so this depends on material this thing is taken care by the constant itself adding a point so delta L is equal to L0 alpha delta t where alpha is coefficient of linear expansion alpha is coefficient of linear expansion it is typically of the order of 10 raise power minus 5 it is very very less and if you see the variation of alpha let's say with temperature this is alpha it goes something like this okay so after 500 Kelvin alpha becomes a constant this proportionality constant alpha even though we are treating it a constant it doesn't remain constant at a lesser temperature it becomes constant after 500 Kelvin or so for a particular material itself okay but then whenever we talk about thermal expansion our temperature will be typically more than this okay so until and unless specified we will assume alpha is a constant for a given material in it out now using this let's say you have a rectangular plate you have a rectangular plate of length L and width V fine you are increasing the temperature by delta t okay coefficient of linear expansion is given as alpha okay initial area is what l into b l into b is the initial area find out the final area when temperature increase by delta t how much delta l will be l alpha delta t okay so l will increase by delta l what will happen to b increase by delta b so b will increase little bit like this so the new rectangle will be like this okay so this much is the extra area that comes in because of the expansion fine I want to find out what is you know new area in terms of l b alpha and delta t assume alpha to be very less