**Problem Statement:**An adiabatic pump is used to compress saturated liquid water at 10 kPa to a pressure of 15 MPa in a reversible manner. Determine the work input per unit mass using the following two approaches:(a) Energy balance (together with property tables)(b) Reversible steady-flow work (*Hint: for the specific volume used in the integral, take the average of the specific volumes at inlet and exit approximately*).**Diagram Explanation:**The diagram illustrates a pump where water enters at a pressure of 10 kPa and is compressed to 15 MPa. The pump is labeled with an arrow indicating the flow of water from the left to the right side of the pump. This visual aids in understanding the direction of the process for analyzing the work input required.

To Find : The work input per unit mass Given : The inlet pressure is The exit pressure is Assumption : Steady operating condition exist Kinetic and potential energy changes are negligible Heat transfer to or from the fluid is negligible Calculation :The properties of water at the inlet of the pump are,The properties of water at the inlet of the pump are,Using the entropy data ,The work done can be obtained as, Using the inlet specific volume the work done can be obtained as, Here error will occur with Using the average specific volume and pressure values, The work done can be obtained as, Here no error will occur The work done is