This is the part that allows the Carnot engine to not violate the 2nd law of thermodynamics, but, hypothetically, why can't we just adiabatically compress the working substance to get it back to State A?
As in, the working substance starts at $A$,
- Isothermal expansion - work is done on the environment
- Adiabatic expansion - work is done on the environment, temperature is decreasing though so the internal energy of the working substance most now be increased in order for the process to be a cycle
- Now use an adiabatic compression to bring the internal energy of the working substance back to that of $A$ so that it can repeat the cycle, without rejecting heat to a cold reservoir.
I know it violates the 2nd law of thermodynamics, but is there explanation for as to why this is impossible other than that?