Question

Why can't a isothermal process occur in a isolated system

Answer 1

in an isolated system the work done by/on the system is zero. heat change is zero. there is no heat and mass transfer

Isothermal process means there can be heat transfer between system and surroundings but tempreture of system during whole process remains constant

If isothermal process is carried out in an isolated system,no heat transfer will be possible.
For isothermal process, it require heat transfer

So,isothermal process can't occur in a isolated system