ENGR266 2022 Q1Past paperOld spec ENGR2662:120 marks24 min

ENGR266 Summer 2022 Q1[VALID]

Answer BOTH parts (a) and (b).

Formulas you may need
  • Ideal gas: PV=nRTPV = nRT (per mole P=RT/VP = RT/V) (on the formula sheet)
  • Redlich-Kwong: P=RTV−b−aT0.5V(V+b)P = \dfrac{RT}{V - b} - \dfrac{a}{T^{0.5}V(V + b)}, a=0.42748R2Tc2.5Pca = \dfrac{0.42748R^2T_c^{2.5}}{P_c}, b=0.08664RTcPcb = \dfrac{0.08664RT_c}{P_c} (learn this; Week 3 slides)
  • van der Waals: P=RTV−b−aV2P = \dfrac{RT}{V - b} - \dfrac{a}{V^2}, a=27R2Tc264Pca = \dfrac{27R^2T_c^2}{64P_c}, b=RTc8Pcb = \dfrac{RT_c}{8P_c} (learn this; Week 3 slides give pcr=a/27b2p_{cr} = a/27b^2, Tcr=8a/27RbT_{cr} = 8a/27Rb)
  • Compressibility factor: Z=PV/RTZ = PV/RT (learn this)
  • Entropy generation for a heat engine between two reservoirs: Sgen=QCTC−QHTH≥0S_{gen} = \dfrac{Q_C}{T_C} - \dfrac{Q_H}{T_H} \ge 0 (from dSiso=dSsys+dSenv≥0dS_{iso} = dS_{sys} + dS_{env} \ge 0) (on the formula sheet)
  • Energy balance for a cycle: W=QH−QCW = Q_H - Q_C (Wnet=Qin−QoutW_{net} = Q_{in} - Q_{out}) (on the formula sheet)
  • Carnot efficiency: η=1−TC/TH\eta = 1 - T_C/T_H (learn this)
  1. (a)
    You are responsible for designing a heat engine. To achieve the required efficiency, the engine's hot reservoir acts at 475∘C475^\circ\mathrm{C} where the molar volume is 0.0001 m30.0001\ \mathrm{m^3}. Using your knowledge of thermodynamics select an appropriate material to construct your engine based on the Maximum Allowable Operating Pressures presented in Table 1. Present all your working and justify any assumptions made. Table 1: Maximum Allowable operating Pressures for a selection of generic materials (MPa): A 20; B 30; C 35; D 42; E 65; F 74. The critical temperature and pressure for the working fluid are 374∘C374^\circ\mathrm{C} and 22.12 MPa respectively and the acentric factor is 0.187.
    [16]
  2. (b)
    Calculate the work done by the engine if the cold reservoir is at room temperature (25∘C25^\circ\mathrm{C}), the total entropy generated during the cycle is 30,000 kJ K−130{,}000\ \mathrm{kJ\,K^{-1}} and the heat deposited from the hot reservoir is 160,000 kJ.
    [4]2:2