1 Thermodynamics (30.0 Points) A cylindric tank contains a cryogenic, binary mixture of nitrogen (index 1) and oxygen (index 2). The tank has a diameter of d = 1.23 m and a height of h = 2.1 m. Due to process data available to you, you know the mass of nitrogen M₁ = 5.84 kg and the mass of oxygen M₂ = 13.68 kg inside the tank. The temperature of the mixture is T = -155.2 °C. Given: . M; in kg kmol Nitrogen 28.01 Oxygen 32.00 Tki in K Pki in bar 126.2 33.9 154.6 50.5 A₁ B₁ Ci 0.040 6.99100 308.365 273.200 0.021 7.11477 370.757 273.200 وليا Binary parameter for nitrogen/oxygen k12 = -0.0104 Universal gas constant R = 8314 kmol K Antoine equation with the parameters A₁, B₁, C₁ log10 Pai = A₁ - B₁ T+C₁ with T in °C, Psi in mbar Tasks: First, you want to know the state your mixture is in. For that purpose, you calculate the pressure p using an equation of state. 1.) Calculate the mole fraction y₁ of nitrogen and the mole fraction y2 of oxygen in the mixture and finally the molar volume of the mixture. (7.0 Points)

Fig: 1