a. Nitrogen can be liquefied using a simple Joule Thomson expansion process. This is done by rapidly and adiabatically expanding cold nitrogen from a high-pressure gas to a low-temperature, low-pressure vapor-liquid mixture. To produce the high pressure, nitrogen initially available at 0.1 MPa and 135 K is reversibly and adiabatically compressed to 2 MPa, isobarically cooled to 135 K, recompressed to 20 MPa, and again isobarically cooled before undergoing the Joule-Thomson expansion to 0.1 MPa. What is the temperature of the liquid nitrogen, and how much compressor work is required per kilogram of liquid nitrogen produced?

b. If, to improve efficiency, the Linde process is used with the same two-stage compressor as in part (a) and with nitrogen vapor leaving the heat exchanger at 0.1 MPa and 125 K, how much compressor work is required per kilogram of liquid nitrogen produced?