Air at $101 \: \mathrm{kPa}$, $15^{\circ} \mathrm{C}$ and $50 \%$ relative humidity is first heated to $20^{\circ} \mathrm{C}$ in a heating coil, and then humidified by spraying water on it. In the final state, the air has temperature of $25^{\circ} \mathrm{C}$ and relative humidity of $85 \%$. The amount of water sprayed (in $\mathrm{gm}$ per $\mathrm{kg}$ of dry air) is $\_\_\_\_\_\_$ (rounded off to two decimal places).
Use the following data: The saturation pressure of water at $15^{\circ} \mathrm{C}=1.7057 \mathrm{kPa}$
The saturation pressure of water at $25^{\circ} \mathrm{C}=3.1698 \mathrm{kPa}$
