 The question was which relation is correct is correct for for N2 gas for N2 gas. The first one is Cp minus Cv is equals to 14 R Cp minus Cv is equals to 28 R Cp minus Cv R by 14 Cp minus Cv is R by 28. Which one is correct? Anyone is getting the answer? Okay, someone is getting 2, 3, 4, all three options I am getting. Okay, see what happens here. In some book what they do? They will write Cp as molar heat capacity and Cp as specific heat capacity. Cp as molar and Cp as specific. Here in this question it is not mentioned that Cp and Cv are molar heat capacity or specific heat capacity. It is not mentioned in that question. If it is molar heat capacity then simply the answer would be Cp minus Cv is equals to R no matter what gas we have. Okay, so usually what happens listen to me carefully molar heat capacity will write down with capital C. This is a capital C so it is capital C molar heat capacity and the smaller one when C is smaller it is specific heat capacity. So since in the question Cp minus Cv is equals to R is not given this is molar heat capacity at constant volume and constant pressure. So since Cp minus Cv is equals to R is not given in the option that only means that this Cp and Cv are specific heat capacity it is not molar heat capacity one thing is that. Now what is the relation of specific heat capacity and molar heat capacity that is what you need to understand. So you tell me this capital C is the molar heat capacity and a small C is the specific heat capacity. This is the specific heat capacity it is defined for one gram one gram it is the molar heat capacity defined for one mole. So one mole we have how many gram the molecular mass of the gas yes or no? Molecular mass of the gas one mole respond guys quickly one mole means molecular mass of the gas isn't it right. So this Cp the capital one the molar one is the molar heat capacity of the mass which is equals to the molecular mass of the gas that is suppose we have nitrogen so this is the molar heat capacity of 28 gram of nitrogen can we say that yes or no CLR you can type in Cp is the molar heat fine ignore this okay ignore this Cp is the molar heat capacity for 28 gram of nitrogen gas fine right. So for one gram we have Cp that is a specific heat capacity so if you multiply this with the molecular mass of the gas M of the gas would it be equals to the molar heat of capacity can we say that how many of you understood this tell me this relation did you understand molar heat capacity is equals to the molecular mass of the gas into a specific heat capacity clear. Similarly can we write down this for can we write down this for the constant volume molar heat capacity at constant volume Cv is equals to the molecular mass of the gas into Cv so capital one is molar the smaller one is specific correct now we know this relation small Cp minus small Cv is equals to R we have that correct so we'll just substitute in terms of you know sorry this minus this equals to R I'll write down so what is given in the question you see in the question we need to find out the expression of specific heat capacity and we know the capital one the capital Cp minus capital Cv is equals to we have R capital Cp is molecular mass of the gas into Cp minus Cv is equals to R so what we can write Cp minus Cv is is equals to R divided by the molecular mass of the gas how many of you understood this tell me this is the formula you can assume you can memorize correct so answer for this question would be what R divided by 28 option D is correct over here option D is correct this formula you must keep in mind this formula you must keep in mind you already know this Cp minus Cv is equals to R then you can substitute this and you'll get the answer okay now you see another thing we were looking at the formula of Cp and Cv relation also we have seen you see this Cv we have a formula is equals to f by 2 into R f is the degree of freedom f is the degree of freedom have you heard about it degree of freedom have you heard about it okay it is not the portion of chemistry it is there in physics you will study the over there if you want I can discuss this okay how to find out but in physics it is not necessary what information you need to know that for different atomicity of gases what would be the degree of freedom I'll write down here just copy this down atomicity and DOF DOF stands for degree of freedom if atomicity is one degree of freedom is three atomicity is two degree of freedom is five atomicity is greater equal to three then degree of freedom is six it is non-linear actually for three molecule must be non-linear so this value you need to memorize degree of freedom stands for the number of different ways by a system can exchange energy with surroundings like for example we see suppose if one is the atomicity means monatomic gas we have helium right so helium can move in along x axis along y axis and along z axis so three different direction it can move so it can exchange energy in three different way that's why we have here degree of freedom three okay you want me to discuss little bit about degree of freedom or you can memorize it tell me yes one second okay I'll do it see degree of freedom you just keep that in mind that it is a different number of ways by which a system can exchange energy with surroundings right different number of ways basically so if you see here we have three types of motion basically I'll go back here again degree of freedom we have three types of or three different way by which a system can exchange energy one is by translational motion another one is rotational another one is vibrational this three type we have generally vibrational motion okay see vibrational motion is inactive at normal temperatures we'll just ignore it inactive at normal temperature it is you know considerable when the temperature is extremely high so we'll just ignore the vibrational motion we're ignoring it correct so degree of freedom because of translational motion is represented by f t because of vibrational is f sorry rotational is f r and because of vibrational is f v so total degree of freedom would be the sum of all these three means total degree of freedom would be f t plus r plus f v this is the total degree of freedom we have here in which f v we are ignoring vibrational we don't consider at normal temperature we are ignoring it correct now if you have a monoatomic gas now we'll see this condition monoatomic gas means atomic city is one monoatomic gas atomic city is one like for example we have helium neon organ etc so like i said the no the monoatomic gas helium can move along x axis can move along y axis can move along z axis the total translational degree of freedom if you count that would be three what would be the rotational degree of freedom rotational degree of freedom is zero over here because you see the atom cannot rotate around its own axis are you getting it in chemistry it is not much there we have the formula of cpcv that formula will calculate with this one degree of freedom so if you want we can discuss it but yes obviously a little bit of idea you must have it's mainly it is there in physics capital f we have here total degree of freedom basically total degree of freedom is equals to this plus this plus this correct okay well once again watch out anyways okay so we have this you see why rotational degree of freedom is zero over here because a molecule cannot rotate about it its own axis rotation is about if we have one molecule and it can rotate about an axis which is not present in the molecule around this the rotation we can consider but single molecule we don't have rotation about any other axis molecule can spin along its own axis like if you if you look at the cricket ball right cricket ball can spin it it cannot rotate we use the word spin over there we don't use the word rotate we call it an office spinner or leg spinner right we don't say off rotator or leg rotator right because one single atom can spin around its own axis it cannot rotate that's why the degree of freedom is zero hence for monoatomic gas the total degree of freedom is three did you get it okay if you have diatomic gas so diatomic gas can obviously exchange energy by three different uh trans transnational motion okay second point you write down diatomic gas so for for monoatomic gas the degree of freedom is three if diatomic gas we have for example we have o2 n2 h2 right we have molecules like this suppose so it can exchange energy along x axis right along y axis along z axis all three axis it can exchange energy and hence it has three translational motion so f t is three here the rotational is what this can rotate not around y axis or around z axis right so it has two rotational degree of freedom so total degree of freedom is five okay for diatomic gas in case of diatomic gas we can also consider linear polyatomic molecule linear polyatomic molecule means all polyatomic molecule which are linear for example co2 we can consider senior co2 has more than two atoms so it is not diatomic molecule but since it is linear its degree of freedom is also five simple one if you have the third one when it is polyatomic gas polyatomic non-linear we have polyatomic non-linear for example so3 so3 this kind of gas we have okay polyatomic non-linear NH3 this kind of gas we have so in this we have all three translational degree of freedom and all three rotational degree of freedom vibrational we are not considering so f value is six over here this is how we calculate degree of freedom for different different molecules now i told you the formula of cv the formula of cv all these formula you need to memorize this is f by two is equals to r for this we do not have any derivation this you need to memorize okay it's the factual thing need to memorize this cv is f by two r so easily we can since we know this f value for different different gases so we can find out cv here easily so you see here if the gases are mono atomic mono atomic f value is three over here the value of cv is cv is three by two r what is the value of cp is five by two r because cp minus cv is equals to r what is the value of gamma gamma is cp by cv that is five by three that is 1.66 copy this down all of you degree of freedom derivation if you don't remember there's no any problem with it but this three formulas three values you must memorize then copy for diatomic could you tell me diatomic easily you can find out the degree of freedom f is equals to what five we have so cv is five by two r so cp of mono atomic becomes cv over here cp is seven by two r and gamma is 1.40 cp by cv clear right and if you did if you if you have polyatomic polyatomic non-linear must you take care of polyatomic non-linear how do you find out molecule is linear or not degree of freedom is six cv is six by two r so three r three r plus r cp is four r and gamma is 1.33 tell me how do we find out whether the molecule is linear or not no yes we can use vsepr find out lone pair and bond pair then we can find out we can find out hybridization and then we can say correct that's the correct way okay so this is it uh there's two more formula we have over here we have done the same formula we are just simplifying it nothing much this cv we can also represent in terms of gamma cv is equals to r by gamma minus one easily you can do this because we know cp minus cv is equals to r and cp by cv is equals to gamma from those two relation you can find out this one more last relation we have gamma is equals to one plus two by f degree of freedom based on the gamma value that we get we have this relation right what we see we have seen that gamma for mono atomic is more than gamma for diatomic is more than gamma for polyatomic okay guys so we'll take a break now after the break we'll start the calculation of work done in different different process how do we calculate work done okay yeah yeah fine so we'll take a break now we'll resume at 625 okay 625 we'll resume take a break yeah