Dry steam is compressed isothermally from 1 bar to 4 bar, with an initial volume of 0.5 m³. The ideal gas law can be applied, specifically using the equation P1V1 = P2V2, since the temperature remains constant. The calculation for the final volume after compression involves substituting the known values into the equation. It is important to consider whether the steam remains in a vapor state or if condensation occurs at intermediate pressures. The discussion emphasizes the need for clarity on temperature and superheat to accurately determine the final volume.