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ENGR5003 / Week 1
ENGR266 2025 Section B Q2Past paperOld spec ENGR2662:212 marks14 min

ENGR266 Summer 2025 Section B Q2[VALID]

The Stirling engine cycle consists of the following steps: 1. Isochoric heating; 2. Isothermal expansion; 3. Isochoric cooling; 4. Isothermal contraction.

Formulas you may need
  • Carnot efficiency: η=1−TCTH\eta = 1 - \dfrac{T_C}{T_H} (learn this; Week 1 slides: Stirling has the Carnot efficiency)
  • Isothermal ideal gas: ΔU=0\Delta U = 0 so Q=WQ = W, W=nRTln⁡V2V1W = nRT\ln\dfrac{V_2}{V_1} (the sheet prints dW=−mRgTln⁡(V2/V1)dW = -mR_gT\ln(V_2/V_1), sic) (on the formula sheet)
  • Boyle's law (isothermal): P1V1=P2V2P_1V_1 = P_2V_2, so V2V1=P1P2\dfrac{V_2}{V_1} = \dfrac{P_1}{P_2} (on the formula sheet)
  1. (i)
    Draw the Stirling cycle on pressure-volume diagram and indicate the direction of the cycle
    [6]Third
  2. (ii)
    If the efficiency of Stirling cycle is 0.43 and heat is absorbed during isothermal expansion at 300∘C300^\circ\mathrm{C}, calculate the heat that is released during the isothermal contraction stage where the pressure increases to 6.3 bar from an initial pressure of 2 bar. You can assume that the thermal efficiency for the Stirling cycle is the same as for the Carnot cycle.
    [6]