(Solved): 1. Helium enters a steady-flow adiabatic compressor at \( 0.6 \mathrm{~kg} / \mathrm{s}, 100 \mathr ...

1. Helium enters a steady-flow adiabatic compressor at \( 0.6 \mathrm{~kg} / \mathrm{s}, 100 \mathrm{kPa} \), and \( 27^{\circ} \mathrm{C} \) with a low inlet velocity and is compressed to \( 600 \mathrm{kPa} \). (a) Determine the exit temperature to make the work input and kinetic energy at the compressor exit have the minimum values. (b) If the rate of work input into the compressor is measured to be a minimum with a value of 1000 \( \mathrm{kW} \), determine the compressor exit velocity, in \( \mathrm{m} / \mathrm{s} \).