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ENGR5003 / Week 1
Week 1 Q1Exercise sheetCurrent specThird12 min

ENGR5003 Week 1 workshop sheet Q1

Describe the following processes: how to draw it in P-V and T-s diagrams.

Formulas you may need
  • Adiabatic (reversible) process: pVγ=constpV^\gamma = \text{const}, TVγ−1=constTV^{\gamma-1} = \text{const} (on the formula sheet)
  • Isothermal ideal gas: pV=constpV = \text{const} (Boyle) (on the formula sheet)
  • Ideal gas entropy change: s2−s1=cvln⁡T2T1+Rgln⁡v2v1=cpln⁡T2T1−Rgln⁡p2p1s_2 - s_1 = c_v \ln\dfrac{T_2}{T_1} + R_g \ln\dfrac{v_2}{v_1} = c_p \ln\dfrac{T_2}{T_1} - R_g \ln\dfrac{p_2}{p_1} (on the formula sheet)
  • Enthalpy of an ideal gas: Δh=cpΔT\Delta h = c_p \Delta T (on the formula sheet)
  • Slope of a constant-property line on T-s: (∂T/∂s)p=T/cp(\partial T/\partial s)_p = T/c_p, (∂T/∂s)v=T/cv(\partial T/\partial s)_v = T/c_v (learn this; follows from T ds=cp dTT\,ds = c_p\,dT at constant pp)
  1. (a)
    Adiabatic
  2. (b)
    Isobaric
  3. (c)
    Isentropic
  4. (d)
    Isochoric
  5. (e)
    Isenthalpic
  6. (f)
    Isothermal