Final answer:
Yes, a gas does work when it expands adiabatically, and the energy for this work comes from the gas's internal energy.
Step-by-step explanation:
When a gas expands adiabatically, it indeed does work. However, since the expansion is adiabatic, there is no heat exchange with the surroundings. The source of the energy needed to do this work is the internal energy of the gas itself. In an adiabatic process for an ideal gas, as the gas does work on its surroundings, the internal energy of the gas decreases, and as a result, the gas cools down. This can be understood from the first law of thermodynamics, which states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. Thus, in the case of an adiabatic expansion, all the work done is at the expense of the internal energy of the gas, leading to dQ = 0 and dEint = -pdV.