An ideal gas system undergoes an adiabatic process in which it expands and does 20 j of work on its environment. how much energy is transferred into the system as heat

Zero.

Explanation:

An adiabatic process is one in which there is no exchange of heat energy. Therefore, in an adiabatic process, heat is neither added to the system not it is removed from the system.

The work done by the gas on the environment is 20 J. This energy is equal to the change in internal energy for an adiabatic process.

Therefore, for an ideal gas to undergo an adiabatic process in which it expands and does 20 J of work on its environment, the heat exchange is zero.