Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?

In an isothermal process for an ideal gas

Can a process on an ideal gas be both adiabatic and isothermal. ?

If heat is supplied to an ideal gas in an isothermal process.

An ideal gas system undergoes an isothermal process, then the work done during the process is

The ideal gas equation for an adiabatic process is

Total internal energy of an ideal gas remains constant in isothermal process.

What is specific heat of a gas is an adiabatic process?

Change in internal energy in an isothermal process for ideal gas is

The specific heat of a gas in an isothermal process is

Statement-1: Two gases at same pressure, volume & temperature are compressed to same volume. The first isothermally and second adiabatically, greater work is done on the gas for an adiabatic process. Statement-2: Final temperature for gas going under isothermal process is more than gas going under adiabatic process.