In a barrel calorimeter, \(5 \mathrm{~kg}\) of steam is sampled at 7 bar. The water equivalent of calorimeter at \(20^{\circ} \mathrm{C}\) is \(10 \mathrm{~kg}\). The barrel contains \(140 \mathrm{~kg}\) of water at \(20^{\circ} \mathrm{C}\). The temperature of water when steam condensed into it was found to be \(40^{\circ} \mathrm{C}\). Calculate the dryness fraction of steam.