In an isothermal process

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

In a isothermal process on an ideal gas, the pressure increases by 0.5% . The volume decreases by about.

Give the equation of state for an isothermal process.

two samples 1 and 2 are initially kept in the same state. the sample 1 is expanded through an isothermal process where as sample 2 through an adiabatic process up to the same final volume.Let p_(1) and p_(2) be the final pressure of the samples and 2 respectively in the previous question then.