 please write down next is specific heat capacity of the gases okay since we are going to deal with gas as our system going forward so we must be knowing you know in detail about how specific heat of gas gases are and how to deal with the gases so that is why this topic okay now when it comes to gases we have already learned in the thermal properties of matter that gas can have two kinds of specific heat isn't it specific heat at constant volume and specific heat at constant pressure okay now when I say only specific heat when I only say the specific heat I mean to say so cv will be equal to 1 by mass into delta q by delta t at constant volume but specific heat has little meaning or you know it is not so useful when it comes to gases so what we define is molar specific heat okay molar specific heat when I just say specific heat I mean to say the specific with respect to mass but when I specify that it is molar then I need to take molar specific heat which is per mole so 1 by n delta q by delta t at constant volume right so delta q at constant volume should be equal to n cv delta t okay and at constant pressure delta q at constant pressure will be equal to similarly n cp delta t okay and there are so many other specific heats possible but as we have learned earlier also only two standard types of specific heats are there okay now why we are doing this topic again as we have done already is to find out the relation between molar specific heat at constant volume and molar specific heat at constant pressure okay so suppose this is the relation I am talking about delta q is equal to delta u plus work done okay now tell me if the change in temperature is delta t between the two states of the gas if change in temperature is delta t for constant volume process for constant volume process okay you need to basically apply this equation okay so things which are given to you are let's say cp is given cv is given molar specific heats are given to you and the pressure is also given to you okay now can you find out what is the when you substitute how this equation transforms all of you please do it how much will be the w zero work done will be zero all all of you agree this work done is integral of pdv and it is constant volume so change in volume is zero dv is zero all the time so that is where the work done is zero okay and delta q is how much at constant volume we can get that from the definition of molar specific heat right since it is a constant volume which is going on I can say delta q is equal to n cv delta t okay so if I substitute these values there I'll get n cv delta t is equal to delta u plus zero so I'm getting delta u is equal to n cv delta t now we have derived this expression of change in internal energy for constant volume okay now suppose the change in temperature is delta t and the process is not constant volume it is some other process but delta t is a change in temperature can I still say that change in internal energy should be this or then I have to derive it again for that process it will be same reason sir internal energy only depends on temperature of the system or change in temperature see in the change in internal energy does not depend on what process you are following okay it only depends on initial location and final location and luckily you have found out change in internal energy for a particular kind of process okay even though you have found out for a particular type of process change in internal energy but since change in internal energy does not depend on what process it is you're going to get the same expression of the change in internal energy for whatever process you assume because it doesn't depend on what process you're following what path you're following it only depends on initial point and the final point okay and hence please write down for ideal gases delta u is equal to n cv delta t for all processes it does not matter what process you are following okay it could be constant pressure constant volume constant temperature it does not matter change in internal energy will be this if delta t is a change in temperature delta u is equal to n cv delta t okay so this is a very powerful equation as you can use it anywhere okay now i am going to apply delta q is equal to delta u plus w for constant pressure okay again things that are given to you cp cv delta t pressure and you can say delta v also if you want to substitute the values over there for constant pressure okay so here it is at constant pressure delta q at constant pressure will be equal to cp delta t right and i know that delta u does not matter what is the process will be always n cv delta t and work done should be equal to pressure into delta v because it is basically integral of p dv since pressure is constant at constant pressure so p comes out of integral it is simply p integral dv which is p into delta v only okay so i will compute the values over there i will get n cp delta t n cp delta t is equal to n cv delta t plus p delta v okay now i can further simplify this because i have a state equation pv is equal to nrt so from here since pressure is constant p delta v will be equal to nr delta t so i can substitute p delta v over there and then i will get this n cp delta t is equal to n cv delta t plus nr delta t okay so from here i will get cp minus cv is equal to r gas constant r okay do you know the value of capital r r is equal to what 8.314 8.314 si units okay in in chemistry you're dealing with liters so that is why the unit is i mean the unit is different and hence the value is different in chemistry in chemistry you might be using 0.0814 anyways now since we have started talking about the processes as in what does process means process means that suppose the state of the system is one initial state is one and the final state is two what process or what path the system is taking to go from initial position to the final position okay that is called a thermodynamic process okay but we will discuss that a little later right now we are going to discuss a couple of more basic things the first is equilibrium state please write down so please write down the definition of equilibrium state it is the it is the state which is completely described completely described by these specific values of some macro variables now what do you mean by micro where macro variable macro variable could be pressure volume temperature density mass internal energy so these all are macro variables so if i'm able to describe what is going on with the system completely by using these macro variables then the system is in equilibrium but what happens is sometimes system is not in equilibrium for example there is this room okay inside this room you light up a fire over here there is let us say fire okay over here there is a fire and you're saying that my entire system is the room the complete room is my system so this is your system boundary okay will the temperature over this zone be same as temperature or that zone will it be same rohnak temperature near the fire will it be same as temperature the corner of the room no right so temperature will be different at different locations of the room arman why do you think it is same temperature so when you light up the gas the temperature near the gas is same as throughout the kitchen then everything inside the kitchen will cook now so temperature at different points in the room are different okay and since temperatures are different how can you describe the temperature of the system what do you call temperature system temperature of this location that location this one this one this one you cannot describe the temperature of your system because at different locations different temperature is there that is why this system is not in equilibrium okay because you cannot describe the temperature of the system although you can you can probably describe the volume of the system but pressure is different at different locations densities will be different okay and internal energy will be different at different locations so that is the reason why you know but then if you talk about the total internal energy that will be same so pressure temperature and density these three things are different at different points on the system so you cannot describe the so I cannot describe the uh temperature of the system because at different location different temperature is there and hence this is not in equilibrium so I cannot study the system because I'm not able to define what is the system's temperature systems pressure systems density okay and hence for a system it is very essential uh that it should be in equilibrium to study it otherwise you don't know what is temperature you don't know what is pressure you don't know what is density okay so there are few examples of uh non-equilibrium states in our textbook for example if this happens there is a let's say piston okay this side is gas and this side is vacuum you're holding this piston right now and then you release the piston what will happen to this piston will it move this way very quickly yes yes it will move quickly that side now when it is moving quickly that side let us say after uh after some milliseconds the piston reaches at the end the distribution in the gas molecule will be something like this it will be still dense over here the molecules uh will be dense over here but the few molecules will be here so you can see that pressure over here is higher than pressure over there I'm talking about immediate okay as soon as the piston moves little bit you're drawing the pressure or you're drawing where the gas molecules are so pressure over here is different from pressure over there so that is the reason why this is not in equilibrium but if you leave the system for very long time then pressure will even out then it will come in equilibrium but right now you cannot define what is the pressure of the system fine now similarly another example is explosion okay so when explosion happens let's say there is a bomb and explosion happens okay so the temperature at different points will be different even the pressure is different at different points because of that you can't even measure or you can't define a system properly if the system is if the thing which is under observation or which you are studying if that is not in equilibrium you cannot find out its pressure its temperature is density uh so many other variables you cannot find out so you cannot study it okay so hence our focus is only those systems which are in equilibrium okay otherwise you can't define the system itself properly right so this is called the equilibrium state