Samples of ethanol are stored in four sealed containers labeled A through D. Each container holds exactly 1.0 mol of ethanol in the phase and at the temperature shown.
A 50 °C liquid ethanol
B 20 °C ethanol vapor (gas)
C –10 °C solid ethanol
D 80 °C liquid ethanol
Assume that each sample remains entirely in the phase indicated and that the containers are rigid.
(a) Rank the samples according to their molar entropy, from greatest to least. If any two samples have approximately equal molar entropy, indicate this clearly.
(b) Provide a detailed justification for your ranking, incorporating both temperature effects and phase differences. Your explanation should refer explicitly to particle-level freedom of motion and distributions of kinetic energy.
(c) Suppose sample A (50 °C liquid) is heated at constant pressure until it reaches 80 °C, becoming sample D. Qualitatively sketch how the entropy of the system changes as a function of temperature over this interval, labeling the relative positions of samples A and D. Explain the shape of your sketch.