Carbon dioxide can be separated from other gases by preferential absorption into an amine solution. The carbon dioxide can be recovered by heating at atmospheric pressure. Suppose pure CO₂ vapor is available from such a process at 80 °C and 1 bar. Suppose the CO₂ is liquefied and marketed in 43-L laboratory gas cylinders that are filled with 90% (by mass) liquid at 295 K. Explore the options for liquefaction, storage, and marketing via the following questions. Use the Peng-Robinson for calculating fluid properties. Submit a copy of the H-U-S table for each state used in the solution.

(a) Select and document the reference state used throughout your solution.

(b) What is the pressure and quantity (kg) of CO₂ in each cylinder?

(c) A cylinder marketed as specified needs to withstand warm temperatures in storage/transport conditions. What is the minimum pressure that a full gas cylinder must withstand if it reaches 373 K?

(d) Consider the liquefaction process via compression of the CO₂ vapor from 80°C, 1 bar to 6.5 MPa in a single adiabatic compressor (η_C = 0.8). The compressor is followed by cooling in a heat exchanger to 295 K and 6.5 MPa. Determine the process temperatures and pressures, the work and heat transfer requirement for each step, and the overall heat and work.

(e) Consider the liquefaction via compression of the CO₂ vapor from 80°C, 1 bar to 6.5 MPa in a two-stage compressor with interstage cooling. Each stage (ηC = 0.8) operates adiabatically. The interstage pressure is 2.5 MPa, and the interstage cooler returns the CO₂ temperature to 295 K. The two-stage compressor is followed by cooling in a heat exchanger to 295 K and 6.5 MPa. Determine all process temperatures and pressures, the work and heat transfer requirement for each step, and the overall heat and work.

(f) Calculate the minimum work required for the state change from 80 °C, 1 bar to 295 K, 6.5 MPa with heat transfer to the surroundings at 295 K. What is the heat transfer required with the surroundings?