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ENGR5003 / Week 4
ENGR217 2018 Q A3Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2018 Q A3[VALID] official answers

Answer ALL parts (a) - (e)

A petrol engine operates on an air-standard Otto cycle, with a compression ratio of 11. At the start of compression, the pressure and the temperature of the air are 1 bar and 303 K respectively.

The compression and expansion of this engine can be assumed as adiabatic. The adiabatic law is given as

PVγ=constantPV^{\gamma} = \text{constant},

TVγ−1=constantTV^{\gamma-1} = \text{constant},

P1−γTγ=constantP^{1-\gamma}T^{\gamma} = \text{constant}, where the variables carry their usual meanings.

Formulas you may need
  • Adiabatic ideal gas: pVγ=constpV^\gamma = \text{const}, TVγ−1=constTV^{\gamma-1} = \text{const} (on the formula sheet, and printed in the question)
  • Constant-volume heat transfer: dQ=mcv dTdQ = m c_v\, dT; isochoric p/T=constp/T = \text{const} (Gay-Lussac) (on the formula sheet)
  • Isothermal ideal gas: dU=0dU = 0 so dQ=dWdQ = dW, ∣W∣=mRgTln⁡(V1/V2)|W| = m R_g T \ln(V_1/V_2) (on the formula sheet)
  • Thermal efficiency: ηth=1−QoutQin\eta_{th} = 1 - \dfrac{Q_{out}}{Q_{in}} (on the formula sheet)
  • Rg=0.287 kJ kg−1 K−1R_g = 0.287\ \mathrm{kJ\,kg^{-1}\,K^{-1}} for air (on the formula sheet)
  1. (a)
    Find the pressure and the temperature of the air at the end of the compression stroke for the isentropic compression with γ=1.4\gamma = 1.4.
    [3]
  2. (b)
    Determine the maximum pressure and the temperature of the cycle, when the heat supplied at constant volume is 1350 kJ kg−11350\ \mathrm{kJ\,kg^{-1}}, and the heat capacity (or the specific heat) is cv=0.88 kJ kg−1 K−1c_v = 0.88\ \mathrm{kJ\,kg^{-1}\,K^{-1}} while heat is added.
    [4]
  3. (c)
    Consider the isentropic expansion with γ=1.33\gamma = 1.33, and the heat capacity cvc_v equal to 0.74 kJ kg−1 K−10.74\ \mathrm{kJ\,kg^{-1}\,K^{-1}} while heat is rejected. Find the heat rejected and the efficiency.
    [4]
  4. (d)
    Assume the compression process to be isothermal rather than isentropic, for the same heat addition as above, γ=1.33\gamma = 1.33 for expansion, cv=0.88 kJ kg−1 K−1c_v = 0.88\ \mathrm{kJ\,kg^{-1}\,K^{-1}} for heat addition and cv=0.74 kJ kg−1 K−1c_v = 0.74\ \mathrm{kJ\,kg^{-1}\,K^{-1}} for heat rejection, determine the new thermal efficiency.
    [5]First
  5. (e)
    Draw the indicator pressure versus volume (P-V) diagrams of: (i) a real cycle, (ii) the Otto cycle. List the main losses neglected in an air-standard Otto cycle, analysing the P-V diagrams.
    [9]