Consider a vessel containing steam at $180^{\circ}C$.The initial steam quality is $0.5$ and the initial volume of the vessel in $1$ $m^{3}$. The vessel loses heat at a constant rate $q$ under isobaric conditions so that the quality of steam reduces to $0.1$ after $10$ hours . The thermodynamic properties of water at $180^{\circ}C$ are (subscript $g$: vapor phase; subscript $f$: liquid phase):
$\begin{array}{cc}\
&\text{specific volume:} & \text{$v_{g}=0.19405m^{3}/kg$,} & \text{$v_{f}=0.001127m^{3}/kg$;} \\
&\text{specific internal energy:} & \text{ $u_{g}=2583.7kJ/kg$,} & \text{ $u_{f}=762.08kJ/kg$;} \\
&\text{ specific enthalpy:} & \text{$h_{g}=2778.2kJ/kg$,} & \text{$h_{f}=763.21kJ/kg$.}\\
\\ \end{array}$
The rate of heat loss $q$ (in $kJ$/hour) is _____________ (rounded off to the nearest integer).