Q.Why should a Carnot cycle have two isothermal and two adiabatic processes?

Step 1. For the Carnot cycle to be maximally efficient, every step in it must be reversible (Section 4.11.1) — any irreversibility anywhere wastes potentially recoverable work.

Step 2. A heat-exchange step is reversible only if it happens isothermally: the working substance must be at the SAME temperature as the reservoir it's exchanging heat with, so no heat crosses a finite temperature gap (which would be irreversible).

Step 3. A step that changes the working substance's temperature (moving it between TH and TC) can only be reversible if it involves no heat exchange at all — i.e. it must be adiabatic — since any heat crossing a temperature difference during that transition would be irreversible. …

Apply the reversibility requirement separately to the heat-exchange steps (must be isothermal) and the te …

Thinking any slow process is automatically reversible — a slow but non-isothermal heat exchange, or a slow adiabatic process with heat leakage, would still be irrever …