In which of the following pairs of cycles, both cycles have at least one isothermal process?

The correct option is Brayton cycle and Rankine cycle.

To understand why both the Brayton cycle and the Rankine cycle can be described as having at least one isothermal process, we analyze the thermodynamic processes involved in each cycle:

1. Rankine Cycle:
In the Rankine power cycle, working fluid (water/steam) undergoes heat addition in the boiler and heat rejection in the condenser. During the phase change transitions (evaporation in the boiler and condensation in the condenser) that occur inside the vapor dome (liquid-vapor saturation region), the pressure and temperature remain constant. Since heat is added and rejected at constant temperature during these phase changes, the cycle contains isothermal processes.

2. Brayton Cycle:
In a modified Brayton cycle featuring multi-stage compression with intercooling and multi-stage expansion with reheating, the thermodynamic path is modified. When the number of intercooling and reheating stages is increased to infinity, the overall compression and expansion processes become isothermal (constant temperature) processes. This thermodynamic optimization allows the modified Brayton cycle to utilize isothermal processes for work transfer, resembling the Ericsson cycle.