In which process is work done equal to heat transferred into the system?

In an isothermal process, the temperature of the system remains constant while heat is transferred into or out of the system. According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Since the temperature remains constant in an isothermal process, the internal energy of an ideal gas does not change, which means that any heat added to the system must be balanced by an equivalent amount of work done by the system.

When heat is transferred into the system, this energy is not used to increase internal energy (as it would in other processes) but is instead converted entirely into work. Therefore, in an isothermal process, the work done on or by the system is equal to the heat that enters the system.

This characteristic distinguishes isothermal processes from others, like adiabatic, isobaric, and isochoric processes, where heat transfer does not equal work done due to variations in internal energy, pressure, or volume. In an adiabatic process, for example, there is no heat transfer, while in isobaric and isochoric processes, the relationships between heat and work differ significantly based on the constraints of volume and pressure