$4\mathrm{.}77$ Figure P$4\mathrm{.}77$ shows a simple vapor power plant operating at steady state with water circulating through the components. Relevant data at key locations are given on the figure. The mass flow rate of the water is $130$ kg$/$s$.$ Kinetic and potential energy effects are negligible. Determine

a$)$ the heat transfer rate to the steam passing through the steam generator, in kW$.$

b$)$ the net power developed for adiabatic operation of the turbine and pump, in k$.$

c$)$ the mass flow rate of the cooling water passing through the condenser, in kg$/$s$,$ if the cooling water experiences a temperature rise of $15\backslash$deg C and negligible pressure drop