A piston-cylinder system contains $2$ kg of wet steam at $90^{\circ} \mathrm{C}$ with quality of $0.1$. The piston is loaded with a linear spring. The steam expands to $800$ kPa and $250^{\circ} \mathrm{C}$ on heating. The work done (in kJ ) in this process is _________ $\text{(rounded off to two decimal places)}$.
Use the following data:
At $90^{\circ} \mathrm{C}: P_{\text {sat }}=70 \mathrm{kPa}, v_{f}=0.001 \mathrm{~m}^{3} / \mathrm{kg}, v_{g}=2.4 \mathrm{~m}^{3} / \mathrm{kg}$
At $250^{\circ} \mathrm{C}$ and $800 \mathrm{kPa}: v=0.29 \mathrm{~m}^{3} / \mathrm{kg}$
