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Steam enters a turbine at $30$ bar, $300^\circ C \: (u = 2750 \: kJ/kg$, $h = 2993 \: kJ/kg)$ and exits the turbine as saturated liquid at $15 \: kPa \: (u = 225 \: kJ/kg$, $h = 226 \: kJ/kg)$. Heat loss to the surrounding is $50  \: kJ/kg$ of steam flowing through the turbine. Neglecting changes in kinetic energy and potential energy, the work output of the turbine (in $kJ/kg$ of steam) is ________
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