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ENGR5003 / Week 1
L3 slide 13: Why does entropy change? Free expansionFrom lectureCurrent spec2:25 marks6 min

ENGR5003 Lecture 3, slide 13 (The reason for the entropy change)

The lecturer asks: "Why does entropy change?" and "Is the entropy related with the work transfer of a reversible process?" The slide then considers an ideal gas that expands freely (into an evacuated space, inside a rigid insulated container) until its volume has doubled.

Formulas you may need
  • Entropy definition: ds=(δqT)revds = \left(\dfrac{\delta q}{T}\right)_{rev} (on the formula sheet)
  • Ideal gas entropy change: Δs=cvln⁡T2T1+Rgln⁡v2v1\Delta s = c_v \ln\dfrac{T_2}{T_1} + R_g \ln\dfrac{v_2}{v_1} (on the formula sheet)
  • Closed-system entropy balance: Δs=sf+sg\Delta s = s_f + s_g, sf=∫δq/Trs_f = \int \delta q/T_r, sg≥0s_g \ge 0 (learn this)
  1. (a)
    List the ways in which the entropy of a system can change, and say whether the work transfer of a reversible process carries any entropy.
    [2]
  2. (b)
    For the free expansion, explain why T2=T1T_2 = T_1 for an ideal gas, and show that Δs=Rgln⁡2>0\Delta s = R_g \ln 2 > 0 even though no heat or mass crosses the boundary.
    [2]
  3. (c)
    [Added] Evaluate the entropy change for 1 kg of air (Rg=0.287 kJ/(kg K)R_g = 0.287\ \mathrm{kJ/(kg\,K)}) whose volume doubles in a free expansion.
    [1]