A piston-cylinder assembly having $250 \: \mathrm{mm}$ diameter contains $0.01 \: \mathrm{kg}$ of water vapor at $1 \: \mathrm{MPa}$ and $200^{\circ} \mathrm{C}$. The specific volume of the vapor is $0.20602 \mathrm{~m}^{3} / \mathrm{kg}$. The system expands as per the relation $\text{p} \text{V}^{n}=$ constant, where $\text{p}$ is pressure and $\text{V}$ is volume. The expansion of water vapour displaces the piston by $50 \: \mathrm{mm}$. If the final pressure is $0.35 \: \mathrm{MPa}$, the value of the exponent $(n)$ is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).
