Five separate processes involving one or more ideal substances occur under the conditions stated.
Process A: 2.0 mol Ar(g), initially at 298 K and 10.0 L, isothermally compressed to 5.0 L.
Process B: 1.0 mol ethanol(l) vaporizes at its normal boiling point, 351 K; $
\Delta H_{\text{vap}} = 38.6\,\text{kJ}\,\text{mol}^{-1}$.
Process C: A partition is removed to mix 1.0 mol Ne(g) with 1.0 mol Kr(g) in a rigid 20 L container at 298 K.
Process D: 1.0 mol N2(g) is cooled at constant volume from 400 K to 300 K.
Process E: 1.0 mol CO2(s) sublimes at 195 K and 1 atm; ΔHsub=25.3kJmol−1.
(a) Without performing detailed calculations, rank the magnitude of the entropy change ∣ΔS∣ for Processes A–E from smallest to largest.
(b) Provide a thorough justification for the ranking in part (a), explicitly addressing how phase, volume, temperature, and mixing each influence matter and energy dispersal.
(c) Derive an expression for ΔS for an isothermal, reversible compression of an ideal gas and use it to calculate ΔS for Process A. Then derive an expression for ΔS for cooling an ideal gas at constant volume and use it to calculate ΔS for Process D. Confirm that the numerical results are consistent with your qualitative ranking.
(d) A student argues that Process C involves no entropy change because the total number of gas moles remains the same. Critically evaluate this claim, citing appropriate reasoning about microstate availability.