Why can't complete heat be converted to work if its vice versa is possible? Is there any proof of why complete heat connot be completed to work rather than the second law of thermodynamics. It might be possible that we are not able to process the heat to complete work at this level.
 A: First of all, I think the title of your post is backwards. It should read:
Why can't heat be completely converted to work if its vice versa is possible
It is theoretically possible to completely convert heat to work for a process. An example is a reversible process isothermal expansion. What is not possible is for a heat engine operating in a cycle to completely convert heat into work. That would be in violation of the Kelvin-Planck statement of the second law which states:
No heat engine can operate in a cycle while transferring heat with a single heat reservoir.
Aside from the second law statement, it can be seen that net work can not be done by a system while only taking heat in. Below is a diagram of the Carnot Cycle. All processes shown are reversible. For simplicity we will assume the system is an ideal gas in a cylinder fitted with a piston.

Process 1-2 is a reversible isothermal expansion  process. The system takes in heat $Q_{IN}$ from a high temperature reservoir and converts it completely to work. The work is the area under the curve 1-2. But this is not a cycle. In order to have a cycle you must return to state 1. Now how can we do this?
On thing we can do is reverse process 1-2 and perform an isothermal compression from 2 to 1. That would complete a cycle, but the net work done would be zero since the work done on the system by the compression equals the work done by the system during the expansion.
So in order to perform net work over a cycle we must return by a different path under process 1-2. For the Carnot cycle this is accomplished by the reversible adiabatic (isentropic) process 2-3, followed by a reversible isothermal compression 3-4 and a reversible adiabatic compression 4-1 completing the cycle.
During the reversible isothermal compression heat $Q_{OUT}$ has to be rejected to a cooler thermal reservoir. The net work done by the cycle is then the area enclosed, or
$$W_{NET}=Q_{IN}-Q_{OUT}$$
So it is not possible to produce net work in a cycle unless some of the heat taken in by the system is rejected. So heat from a single reservoir can not be completely converted to work in a cycle.
Hope this  helps.
A: Work can be converted to heat by friction.  Problems arise when you want to convert heat to work.  This involves having some material which expands when heated. Some of the heat energy flowing into the material comes out as work, and part increases the internal energy of the material (or is lost to friction).  This gives a limited amount of work.  If you want more you have to start over, either by removing the extra internal energy or by discarding the heated material and bringing in fresh (cold) material.  Either way, some of your energy goes to waste. The efficiency increases if you can work with  a larger temperature difference.
