$4\mathrm{.}51.$ Air enters a compressor operating at steady state with a volumetric flow rate of $37$ m$^3/$min at $136$ kPa, $305$ K and exits with a pressure of $680$ kPa and a specific volume of $0\mathrm{.}1686$ m$^3/$kg$.$ The work input to the compressor is $161\mathrm{.}5$ kJ per kg of air flowing. Energy transfer from the air to cooling water circulating in a water jacket enclosing the compressor results in an increase in the temperature of the cooling water of $11\backslash$deg C with no change in pressure. Neglecting heat transfer from the outside of the jacket as well as all kinetic and potential energy effects, what is the mass flow rate of the cooling water, in kg$/$min$?$