Problem $5(10$ points$)-$ Energy Balance on a turbo$-$pump assembly

A water pump is driven by a turbine through a common shaft. Steam enters the turbine at $1$ MPa and

$300C$ and leaves at $150$ kPa and a quality of $0\mathrm{.}98.$ Saturated liquid water enters the pump at $20C$ at a

mass flow rate of $100,000k\frac{g}{h}$ and leaves the pump at $10$ MPa $.$ Please answer the following questions

considering that processes in both devices are adiabatic and changes in kinetic and potential energy can

be neglected.

a$.$ Create a schematic for the installation and indicate the boundaries for the fluids passing through

the pump and turbine if you were to perform a mass and energy balance on those devices. Use

the correct graphic representation for a turbine and for a pump.

b$.$ Considering that all the power produced by the turbine is taken by the pump, determine the

mass flow rate of steam needed at the inlet of the turbine, in $k\frac{g}{h}.$ Hint: Consider that the

power produced by the turbine is transferred to the pump.

c$.$ Considering that the efficiency in transferring power from the turbine to the pump is $80\%,$

determine the mass flow rate of steam needed at the inlet of the turbine, in $k\frac{g}{h}.$