Heat and Mass Transfer

The water activity of dried skim milk powder at a constant moisture content of $m = 0.05\text{ kg water/kg dry solid}$ is $a_{w,1} = 0.20$ at $T_1 = 20.0^\circ\text{C} = 293.15\text{ K}$. The net isosteric heat of sorption is $q_{st} = 15.0\text{ kJ/mol} = 15000\text{ J/mol}$ ($R = 8.314\text{ J/(mol}\cdot\text{K)}$). Using the integrated Clausius-Clapeyron equation: $\ln\left(\frac{a_{w,2}}{a_{w,1}}\right) = -\frac{q_{st}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$, the water activity at $T_2 = 40.0^\circ\text{C} = 313.15\text{ K}$ is ________ (round off to three decimal places).