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ENGR5003 / Week 4
Old spec L18 Question 1TutorialOld spec ENGR2172:215 min

ENGR217 (old spec) Thermo L18 tutorial, Question 1 official answers

Complete the following table for the ideal Otto cycle. The compression ratio is 5 and the specific heat supplied is 750 kJ/kg. Assume 1 kg of air, γ=1.4\gamma = 1.4, cv=0.7175c_v = 0.7175 kJ/(kg K) and Rg=0.287R_g = 0.287 kJ/(kg K). What is the net work output and the thermal efficiency?

Statep (bar)V (m3)T (K)
11?300
2???
3???
4???

(The same question is Question 1 in the current ENGR5003 Week 5 Lecture 15.)

Formulas you may need
  • Ideal gas pV=mRgTpV = mR_gT (on the formula sheet)
  • Adiabatic process: pVγ=constpV^\gamma = \text{const}, TVγ−1=constTV^{\gamma-1} = \text{const} (on the formula sheet)
  • Constant-volume heat addition qin=cv(T3−T2)q_{in} = c_v(T_3 - T_2) (on the formula sheet)
  • Adiabatic work Wab=pbVb−paVaγ−1=mcv(Tb−Ta)W_{ab} = \dfrac{p_bV_b - p_aV_a}{\gamma - 1} = mc_v(T_b - T_a) (magnitude) (on the formula sheet)
  • Otto efficiency η=1−1rvγ−1\eta = 1 - \dfrac{1}{r_v^{\gamma - 1}} (on the formula sheet)
  1. (a)
    Complete the table.
  2. (b)
    What is the net work output and the thermal efficiency?