Question

if internal energy of an ideal gas decreases by same amount . as the work done by system, the process is

Answer 1

change in internal energy=work done+heat exchange
change in internal energy=work done if process has no heat exchange, i.e. it's adibatic.
(q=0)

Answer 2

Answer: adibatic

Explanation: According to first law of thermodynamics:

$\Delta U=q+w$

$\Delta U$=Change in internal energy

q = heat absorbed or released

w = work done on or by the system  =$-P\Delta V$  

$\Delta U=q-p\Delta V$

If internal energy changes by the same amount as the work done, heat absorbed or released is zero, thus the heat remains constant i.e. adiabatic process.