 Welcome back. What we have shown now, it is something important. We have shown that given temperature levels T1 and T2 such that T1 is not equal to T2 and an engine working between T1 and T2 such that it absorbs heat from the reservoir at T1, rejects heat the reservoir at T2, Q1 and Q2 respectively and produces a positive amount of work. Then when it comes to heat flow from T1 to T2 is possible but it is not possible to have any heat flow such that the heat flow takes place by itself from the reservoir at T2 to the reservoir at T1. This gives us a hint about the thermodynamic idea of a higher temperature and lower temperature. At this stage we are tempted to say that let us say temperature T1 is higher than temperature T2 because that is the general feeling. Our temperature levels traditionally are measured by numbers such that so-called hotter stuff has a higher number associated with it. But there is no thermodynamic basis for it. Here we are finding a thermodynamic basis. We can say perhaps we have not yet confirmed it that given two temperature levels T1 and T2 unequal to each other that temperature say T1 is higher provided an engine will work by absorbing heat from T1 and rejecting it to T2 and that automatically means that if you allow direct heat transfer between two systems say one at T1 and another at T2 then heat flow will take place from T1 to T2. Heat flow will not take place from T2 to T1. So the question is can we say T1 greater than T2 in a thermodynamic sense. Before we jump to this conclusion we have to show that for this to be 2 it should be mathematically consistent. For example given two numbers the greater than link it is such that let us say we have three numbers A, B, C. A is greater than B, B is greater than C then mathematics tells us that A must be greater than C. Remember that in math if A is greater than B and if B is greater than C then A is greater than C. Do we have the same relation between temperature levels that is something we have to show before accepting this definition of a higher temperature and lower temperature. Thank you.