 Welcome back. We now look at the Karatheodore's form or Karatheodore's statement of this first law of thermodynamics. For this what we consider is a system which is an adiabatic system. We consider some system which is adiabatic that means all parts of the boundary of this system are adiabatic and that means only work interaction can take place of any kind and because it is adiabatic let us say that the work done is WAD indicating that we are looking at specifically an adiabatic system. Then we consider various processes of this system. You may write PV or you may write some thermodynamic variable Y there some thermodynamic variable X here and let us consider an initial state 1 and a final state 2. And let us consider a few different processes executed by this system. For example one process could be like this. This is a quasi-static adiabatic process. Another quasi-static adiabatic process could be like this. A third quasi-static non-quasi-static adiabatic process could be like this. This is just a representation. The path does not matter. So we notice here that we have fixed initial and final states 1, 2. We are considering different processes between the same initial and final state 1, a 2, 1, b 2, 1, c 2. We consider all must be adiabatic. Now Karate-Odori's statement says that this work adiabatic work from initial state 1 to a final state 2 is independent path and details of the process. This means that if our process is adiabatic and if the initial state and final state are fixed then the work done does not depend on which path we took, whether we took 1 a 2 or whether we took 1 b 2 or whether we took 1 c 2. It also does not depend on whether the process is quasi-static or not, whether during the process one mode of work was used or another mode of work was used or a combination of the modes was used. All we need is that the initial and final states are fixed. If those two are fixed, well and the process is adiabatic, the work done would be the same. This is our statement of the first law of thermodynamics, absolute basic statement as provided by Karate-Odori. Now what does this imply? Let me again write down. If we have an adiabatic system, if we have fixed initial and final states 1 and 2 then W adiabatic of 1 to 2 is the same for all such, that means adiabatic processes and that means if we write this in an integral form, integral 1 to 2 dW adiabatic, whether one can evaluate it or not, one can evaluate it if the process is quasi-static, one may not be able to evaluate it if the process is non-quasi-static, then this is independent of the path. This implies mathematically that dW adiabatic must be an exact differential and we know that only properties can have exact differentials. So this implies that the integral of this dW adiabatic from 1 to 2 must represent the change in some thermodynamic property. Thank you.