Q3(c)(ii). Expansion of an ideal gas into a vacuum in an insulated box
A thermally insulated box is separated into two compartments (volumes V₁ and V₂) by a membrane. One of the compartments contains an ideal gas at temperature T, the other is empty (vacuum). The membrane is suddenly removed, and the gas fills up the compartments and reaches the equilibrium. What is the final temperature of the gas? Show that the gas expansion process is irreversible. [diagram of the insulated box given in the paper]
Answer in brief
Final temperature = T (unchanged), because q = 0 and w = 0, so ΔU = 0; the expansion is irreversible because ΔSuniv = nR ln[(V₁ + V₂)/V₁] > 0.
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Coversfree expansionJoule expansionentropy changeirreversible processsecond law of thermodynamics
All parts of Question 3
- 3(a) Surface energy when one drop is split into 125 drops10 marks
- 3(b) Ion-selective electrodes; pH with the glass electrode20 marks
- 3(c)(i) Enthalpy of vaporisation from the triple point to the critical point10 marks
- 3(c)(ii) Expansion of an ideal gas into a vacuum in an insulated box10 marks