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ENGR5003 / Week 1
ENGR266 2018 Q A2Past paperOld spec ENGR2662:125 marks30 min

ENGR266 Summer 2018 Q A2[PARTIAL] official answers Left out: Nothing is left out: all parts (a)-(e) are transcribed. Tagged PARTIAL because the coefficient of performance of a refrigerator (Carnot refrigeration cycle) is not explicitly in the current slides; the current slides cover the Carnot engine, entropy and ideal-gas processes, from which the reversed cycle follows directly.

Answer ALL parts (a) - (e).

Formulas you may need
  • Adiabatic ideal gas: TVγ−1=constTV^{\gamma-1} = \text{const}, pVγ=constpV^\gamma = \text{const} (on the formula sheet)
  • CV=Rγ−1C_V = \dfrac{R}{\gamma - 1}; adiabatic work W=CV ΔTW = C_V\,\Delta T (from dU=dQ−dWdU = dQ - dW with dQ=0dQ = 0) (on the formula sheet)
  • Isothermal ideal gas: dU=0dU = 0, Q=W=RTln⁡(V2/V1)=RTln⁡(P1/P2)Q = W = RT\ln(V_2/V_1) = RT\ln(P_1/P_2) (on the formula sheet)
  • Entropy change of an ideal gas: ΔS=Cpln⁡(T2/T1)−Rln⁡(P2/P1)\Delta S = C_p\ln(T_2/T_1) - R\ln(P_2/P_1); reversible dS=dQ/TdS = dQ/T (on the formula sheet)
  • Carnot refrigerator: COPR=QLWin=TLTH−TLCOP_R = \dfrac{Q_L}{W_{in}} = \dfrac{T_L}{T_H - T_L} (learn this; not explicitly in the current slides)
  1. (a)
    Draw a Carnot refrigeration cycle on a P-V diagram indicating the direction of the cycle, where heat enters and is rejected from the system as well as the values of the polytropic indices for each of the processes.
    [6]2:2
  2. (b(i))
    In a Carnot refrigerator the working fluid enters the compressor with an initial molar volume of 0.002 m3 mol−10.002\ \mathrm{m^3\,mol^{-1}} at a pressure of 100 kPa and a temperature of −21∘C-21^\circ\mathrm{C}. In the compressor the molar volume of the working fluid is reduced to 0.0013 m3 mol−10.0013\ \mathrm{m^3\,mol^{-1}}. Assume the working fluid is an ideal gas with a heat capacity ratio CP/CV=1.5C_P/C_V = 1.5, calculate: (i) The coefficient of performance (COP) for this Carnot cycle.
    [6]
  3. (b(ii))
    (ii) The work done by the compressor.
    [6]
  4. (c)
    Draw the Carnot refrigeration cycle on a T-S diagram.
    [2]Third
  5. (d)
    What is the total change in entropy during the Carnot refrigeration cycle?
    [1]Third
  6. (e)
    Calculate the entropy change during the reversible isothermal expansion process if the pressure, when the working fluid starts the process, is 110 kPa. Assume the working fluid is an ideal gas.
    [4]