 Welcome back. It is time for us to look at not only engines and refrigerators in a qualitative way but look at them in some quantitative way. So let us look at their performance parameters. For an engine for example for a 2T heat engine which I will sketch but in general for any engine we have the heat supply Q1, the heat rejected Q2 and the work output W. The two temperatures T192 are such that T1 is greater than T2. Now here the work output W is what we want. Whereas the Q1 the heat supply is what needs to be supplied. In an actual engine work represents the power output and that is what we need. Whereas Q1 represents the energy released by the fuel and we have to pay for the fuel. So here the performance parameter is the efficiency defined as W by Q1. It is a ratio, it is a dimensionless number. We can represent it either as a fraction like 0.2, 0.3, 0.4 or as a percent like 20%, 30% or 40%. When it comes to a refrigerator and what I am going to show is a refrigerator which you may call a 2T refrigerator. We need to extract Q2 from the low temperature system at T2. We have to provide work, this is what is supplied and of course Q1 which should by first law equals Q2 plus W will be rejected by T1. In a typical refrigerator or freezer this Q2 extracted from the low temperature system will reduce its temperature, make vegetables and whatever is contained in the cooler it will freeze water into ice, maintain the consistency of ice cream at low temperature. This W represents the electricity consumption, the power consumed to maintain this flow Q2. So this is what we want, this is what needs to be supplied for it to work. So here the corresponding ratio as a performance parameter will be Q2 by W and this will call the coefficient of performance. The common symbol is not a symbol but an acronym short form it is COP. Again you will notice that the Kelvin Planck statement of the second law dictates that this efficiency can never be 1, it has to be less than 1. Similarly we know that here W cannot be 0, so the COP has to be a finite number. Now the second law limits efficiency less than 1 COP a finite number are qualitative. For example can we have an engine with an efficiency less than 1 but say something like 0.999 almost 100% but not 100%, 99% plus can we have a refrigerator with not infinite coefficient of performance but say coefficient of performance of say 1000 or 500. The question now are there other limits more restricted on efficiency of an engine and COP of refrigerator. This is a question which we should now look at and before we can answer that question we have to look at what we call the Carnot theorem. One of the most important principles in thermodynamics but before we approach and state and prove the Carnot theorem there is one very important word and adjective that we have to define and that is a reversible process. This is what we will do now. Thank you.