It is impossible to cross two adiabatic curves. Could someone better justify me why? Is it something related to the Second Law?
Two adiabatic curves can intersect, but one of the adiabatic processes has to be irreversible. If both processes are carried out quasi-statically, then the irreversible process involves friction (a process can be quasi-static but irreversible due to friction). To illustrate, let's assume an ideal gas undergoes two adiabatic processes, one irreversible due to friction and one reversible.
For any adiabatic process, applying the first law
And since for any ideal gas, any process
Although in an adiabatic process there is no heat transfer between the system and the surroundings, if the process involves friction that will result in an increase in internal energy as if heat were transferred to the gas. Since for an ideal gas the internal energy depends only on temperature, as indicated above, the final temperature for a given final volume will be higher for the process with friction and thus the decrease in internal energy will be less, and less work performed for the adiabatic process with friction.
The diagram below shows a reversible and irreversible (due to friction) adiabatic process for an ideal gas, both starting with the same initial conditions. That is the one point where the two processes intersect, or "cross".