Partially saturated air at $1 \; \mathrm{bar}$ and $50^{\circ} \mathrm{C}$ is contacted with water in an adiabatic saturator. The air is cooled and humidified to saturation, and exits at $25^{\circ} \mathrm{C}$ with an absolute humidity of $0.02 \mathrm{~kg}$ water per kg dry air. Use latent heat of vaporization of water as $2450 \mathrm{~kJ} . \mathrm{kg}^{-1}$, and average specific heat capacity for dry air and water, respectively as $1.01 \mathrm{~kJ} \cdot \mathrm{kg}^{-1} \mathrm{~K}^{-1}$ and $4.18 \mathrm{~kJ} . \mathrm{kg}^{-1} \mathrm{~K}^{-1}$. If the absolute humidity of air entering the adiabatic saturator is $\mathcal{H} \times \mathbf{1 0}^{-3} \; \text{kg}$ water $\text{per kg}$ dry air, the value of $\mathcal{H}$ is____________(rounded off to two decimal places).