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ENGR5003 / Week 3
ENGR266 2023 Q A1Past paperOld spec ENGR2662:125 marks30 min

ENGR266 Summer 2023 Q A1[PARTIAL] official answers Left out: Part (a) asks for the purpose and operation of a refrigeration cycle, which is not in the current slides. Parts (b)-(d) (R134a tables, Redlich-Kwong) are on-syllabus.

Answer ALL parts (a) - (d).

Figure A1-1: A thermodynamic cycle on a temperature - entropy phase diagram.
Figure A1-1: A thermodynamic cycle on a temperature - entropy phase diagram.
Formulas you may need
  • Wet-mixture property: s=(1−x)sf+xsgs = (1 - x)s_f + x s_g, x=mg/mtotalx = m_g/m_{total} (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)
  • Energy balance for a refrigeration cycle: QH=QL+WinQ_H = Q_L + W_{in}, COPR=QL/WinCOP_R = Q_L/W_{in} (learn this)
  1. (a)
    In your own words describe the purpose and operation of the thermodynamic cycle presented in Figure A1-1.
    [8]
  2. (b)
    Assuming the cycle is using HFC-134a, use the data tables to calculate the liquid fraction at point 4 in the cycle assuming it has an entropy of 1.4 kJ kg−1 K−11.4\ \mathrm{kJ\,kg^{-1}\,K^{-1}} and a temperature of −35∘C-35^\circ\mathrm{C}?
    [6]2:2
  3. (c)
    Calculate the pressure at point 1 using the Redlich-Kwong equation of state if the temperature is 150∘C150^\circ\mathrm{C} and the volume is 0.006 m3 mol−10.006\ \mathrm{m^3\,mol^{-1}}. The critical temperature for HFC-134a is 101.08∘C101.08^\circ\mathrm{C} and the critical pressure is 4060.3 kPa.
    [7]2:2
  4. (d)
    What are the deficiencies of the Redlich-Kwong equation of state and what can be done to address these?
    [4]2:2