Is the reversible process possible? When I was studying about heat engine, specifically Carnot cycle, I though the assumptions to be impossible. Then why one should study all these? What would reversibility mean in reality?
 A: This is a very important question, thermodynamics strictly speaking only applies to quasistatic processes. E.g. if heat is transferred from one system to another one, then that process is necessarily an out of equilibrium process during which you cannot rigorously define thermodynamic variables like temperature (not just one temperature for the entire system, obviously you would want to describe this using two temperatures, but even that is not possible). Only when the process happens infinitely slowly, is a thermodynamic description of the heat transfer process possible.
As Frederick Reif says in his book, thermodynamics is a misnomer, the subject should have been called "thermostatics". So, how can be that thermodynamics is such a useful subject and used by engineers to describe real physical processes when the theory itself says that it only applies to static equilibrium situations?
The reason why you can use thermodynamics in practice is because in many cases it suffices to consider initial and final states that are in thermal equilibrium. So, in a Carnot-like process that is not an ideal reversible Carnot process, you can still consider a rigorously defined initial state where you have two objects that are at different temperatures and the heat engine in a well defined thermodynamic state. And you can consider a final state with the machine in the same state as in the initial state and the two objects in well defined thermal equilibrium states but now at different temperatures compared to their initial temperatures.
Work and heat are well defined from only the initial and final states. Work is defined as the change in internal energy due to a change in the external parameters and this does not require that there be a thermodynamic description of the process. Heat is defined as the part of the change in internal energy that is not due to work. The First Law of thermodynamics is thus a trivial consequence of conservation of energy.
Another important aspect of thermodynamics is that the way you can define the system is entirely subjective, which allows you some flexibility to be able to describe processes that are out of equilibrium. E.g. if you have two systems each of which is in thermal equilibrium but at different temperatures, then the system comprising of both of them is not in thermal equilibrium and thus cannot be described by a single temperature.
You can then ask if you can reverse this process, where an out of equilibrium system can be considered as a collection of subsystems that are each in internal thermal equilibrium but not in equilibrium with each other. In general this doesn't work, but to a good approximation you can usually describe an object like a gas that is not in thermal equilibrium as being in "local thermal equilibrium". You then assume that there exists a position dependent temperature, pressure etc. To a first approximation you can capture all the effects of the non-equilibrium using so-called transport coefficients like heat conducion coefficient, viscosity, etc. that describes how the system wants to relax back to global thermal equilibrium.
That such a description is not exactly valid becomes clear if you attempt to compute the transport parameters from first principles. You'll find that if you assume that each point really has a locally well defined temperature, then you would not have any heat conduction, so the heat conduction coefficient should be zero. It is only nonzero because the local velocity distribution is not given exactly by the Maxwell Boltzmann velocity distribution corresponding to the local temperature (or for that matter any temperature).
