A 2.0 mol sample of an ideal monatomic gas is confined in a frictionless piston–cylinder apparatus at 300 K. The gas is allowed to change volume while the external temperature is held constant at 300 K.
Initially the volume is 2.0 L.
After the process the volume is 4.0 L.
A student claims, “Because the gas particles are now twice as far apart, the entropy of the gas must have decreased to half its original value.”
(a) Identify the sign (positive, negative, or zero) of the entropy change, ΔS, for the gas during this process and briefly state the criterion you used.
(b) Describe, at the particulate level, how the spatial distribution of gas molecules changes during the expansion and relate this change to the concept of matter dispersal.
(c) Using thermodynamic reasoning, refute the student’s claim that the entropy decreases to half its original value. Your explanation should address both the direction and the relative magnitude of the entropy change.
(d) Predict qualitatively how the magnitude of ΔS for an isothermal expansion from 2.0 L to 3.0 L would compare with the expansion from 2.0 L to 4.0 L, and justify your prediction without performing a numerical calculation.