Under what conditions can an ideal gas undergo a change of state without doing external work?

Nswer 

Work done = Pressure * ΔV [ change in volume ] 

If ΔV=0, then no work is done 

Zero work thermodyanamic process is called ' isochoric process.' 

For example if a gas heated in a rigid container: the pressure and temperature 
of the gas will increase, but the volume will remain the same. 

This is called an isochoric thermodynamic process. 

It is actually possible to do work on a system without changing the 
volume, as in the case of stirring a liquid

The objects are acted upon by only one force. gravity. mass times the acceleration of gravity (-9.81meters/second squared).