The volume of the iron piece is 2 dm3. To calculate the Archimedes' buoyant force acting on the iron piece when it is fully submerged in water or alcohol, we need to know the density of the liquid.

The buoyant force (Fb) can be calculated using the formula:
Fb = ρ * g * V

Where:
- ρ is the density of the liquid
- g is the acceleration due to gravity (approximately 9.8 m/s2)
- V is the volume of the submerged part of the object

The buoyant force is equal to the weight of the liquid displaced by the object. Therefore, the buoyant force will be different in water and alcohol because their densities are different.

If the iron piece is submerged at different depths, the volume of the submerged part will change, and hence the buoyant force will also change. The deeper the iron piece is submerged, the larger the volume of the submerged part, and therefore, the larger the buoyant force.

In conclusion, the Archimedes' buoyant force acting on the iron piece will change depending on the density of the liquid and the depth at which it is submerged.