What is the cooling-water rate per intercooler?

What is the ideal work for the compression process of Ex. 7.9? What is the thermodynamic efficiency of the process? What are SG and Wlost? Take Tσ = 293.15 K.

Air at 1(atm) and 35°C is compressed in a staged reciprocating compressor (with

intercooling) to a final pressure of 50(atm). For each stage, the inlet gas temperature is

35°C and the maximum allowable outlet temperature is 200°C. Mechanical power is

the same for all stages, and isentropic efficiency is 65% for each stage. The volumetric

flow rate of air is 0.5 m3⋅s−1 at the inlet to the first stage.

(a) How many stages are required?

(b) What is the mechanical-power requirement per stage?

(c) What is the heat duty for each intercooler?

(d) Water is the coolant for the intercoolers. It enters at 25°C and leaves at 45°C.

What is the cooling-water rate per intercooler?

Assume air is an ideal gas with CP = (7/2)R.