A cylinder fitted with a movable piston contains \(1 \mathrm{~kg}\) of steam at an initial pressure of \(6 \mathrm{bar}\) and of volume \(0.26 \mathrm{~m}^{3}\). Determine the dryness fraction of steam.

If steam expands according to the law \(p v^{n}=c\), to a final volume of \(0.52 \mathrm{~m}^{3}\) and the pressure is \(2.5 \mathrm{bar}\), calculate the value of index \(n\) and the work done during expansion.