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ENGR5003 / Week 2
ENGR266 2021 Q1Past paperOld spec ENGR2662:119 marks23 min

ENGR266 Summer 2021 Q1[PARTIAL] Left out: Parts (b)-(c) need the Pitzer second-virial correlation and the generalised compressibility chart, which are not in the current slides or formula sheets (only Z, van der Waals and Redlich-Kwong are taught).

Answer ALL parts (a) - (c).

Formulas you may need
  • SFEE: Q˙−W˙=m˙[(h+C22+gZ)out−(h+C22+gZ)in]\dot Q - \dot W = \dot m\left[(h + \tfrac{C^2}{2} + gZ)_{out} - (h + \tfrac{C^2}{2} + gZ)_{in}\right] (on the formula sheet)
  • Liquid enthalpy change: Δh=cpΔT\Delta h = c_p \Delta T (from dQ=mcpdTdQ = m c_p dT, cp=(∂h/∂T)pc_p = (\partial h/\partial T)_p) (on the formula sheet)
  • Compressibility factor: Z=PVRTZ = \dfrac{PV}{RT}, reduced properties Tr=T/TcT_r = T/T_c, Pr=P/PcP_r = P/P_c (learn this)
  • [EXTERNAL] Pitzer second-virial correlation: Z=1+B^PrTrZ = 1 + \hat B \dfrac{P_r}{T_r}, B^=B0+ωB1\hat B = B^0 + \omega B^1, B0=0.083−0.422Tr1.6B^0 = 0.083 - \dfrac{0.422}{T_r^{1.6}}, B1=0.139−0.172Tr4.2B^1 = 0.139 - \dfrac{0.172}{T_r^{4.2}} (learn this; not in the current materials)
  • [EXTERNAL] Lee-Kessler corresponding states: Z=Z0+ωZ1Z = Z^0 + \omega Z^1 with Z0,Z1Z^0, Z^1 read from the Lee-Kessler tables (learn this; not in the current materials)
  1. (a)
    Water in a tank at 87∘C87^\circ\mathrm{C} is pumped into a second tank that is located 20 m above the initial tank at a rate of 6.5 kg s−16.5\ \mathrm{kg\,s^{-1}}. The pump does 500 kJ s−1500\ \mathrm{kJ\,s^{-1}} of work and the water loses 300 kJ s−1300\ \mathrm{kJ\,s^{-1}} of heat during the transfer. Assuming that the specific heat of water is CP=4.186 kJ kg−1C_P = 4.186\ \mathrm{kJ\,kg^{-1}}, calculate the temperature of the water in the second tank, stating any assumptions made.
    [7]2:2
  2. (b(i))
    Calculate the compressibility factor for methanol at a temperature of 393∘C393^\circ\mathrm{C} and a pressure of 404.85 bar using the Pitzer Correlation for the Second Virial Coefficient. For methanol the critical temperature and pressure are 239.5∘C239.5^\circ\mathrm{C} and 80.97 bar respectively and the acentric factor is 0.354.
    [6]2:2
  3. (b(ii))
    Calculate the same compressibility factor using the theorem of corresponding states.
    [2]2:2
  4. (c)
    Comment on differences between the two numbers and discuss their reliability.
    [4]