Liquid nitrogen is useful for medical purposes and for research laboratories. Determine the minimum shaft work needed to liquefy nitrogen initially at 298 K and 0.1013 MPa and ending with saturated liquid at the normal boiling point, 77.4 K and 0.1013 MPa. The heat of vaporization at the normal boiling point is 5.577 kJ/mol, and the surroundings are at 298 K. The constant pressure heat capacity of gaseous nitrogen can be assumed to be independent of temperature at 7/ 2R for the purpose of this calculation.

(a) Consider nitrogen entering a flow device at 1 mol/min. Give shaft work in kW.

(b) Consider nitrogen in a piston/cylinder device. Give the work in kJ per mole liquefied.

(c) Compare the minimum shaft work for the two processes. Is one of the processes more advantageous than the other on a molar basis?