According to maximum work theorem work done maximum work is done during reversible process . consider a reversible adiabatic and irreversible adiabatic process that occurs between two states of the system. Now work done in an irreversible adiabatic process is less. Change in internal energy is same for both the process. No heat is exchanged in both the process , since the process is adiabatic. Doesn't this violate 1st law?
If you carry out an irreversible adiabatic process starting out at state A and ending at state B, you will not be able to identify a reversible path between the same two states that does not involve an exchange of heat with the surroundings. In other words, there is no adiabatic reversible path between states A and B.
Here is the simplest example I can think of to illustrate this. I have two identical cubes of material.
State 1: One cube at $T_h$ and the other at $T_c$
State 2: Both cubes at $(T_h+T_c)/2$
I can easily identify a process for getting from State 1 to State 2 irreversibly. You just put the two cubes into contact with one another and allow them to equilibrate.
I can also think of a simple process to get the system from State 1 to State 2 reversibly, but not without exchanging heat with the surroundings. Try to figure out a way of doing it. You won't be able to.