Read Entropy Signs Before Predicting Spontaneity
Second-law questions ask you to track a sign — of ΔS, of ΔG, or of a volume/entropy change on a phase transition — more often than they ask you to compute a number.
Second Law: Entropy, Spontaneity & Gibbs Energy is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Cyclic processes: ΔU returns to zero, entropy doesn't have to
but individual reversible adiabatic segments within that cycle can have zero entropy change while still having nonzero internal-energy change, since Q=0 for an adiabatic step doesn't mean ΔU=0 for that step.
Steam condensing into liquid water: entropy and volume both fall
When steam mixes with liquid water in an isolated system, the system's entropy and volume both decrease as vapour condenses — predicting the sign correctly means recognising condensation as the spontaneous direction here, driven by the surroundings' entropy increase outweighing the system's own entropy decrease.
Reading ΔG° = -RT ln K vs temperature graphs
A plot of RT ln K (or ln K) against T lets you read off the sign and rough magnitude of ΔH° and ΔS° from its slope and intercept, and the temperature range where the reaction is spontaneous (ΔG°<0, i.e. where K>1) directly from where the curve crosses zero.
Intensive properties don't depend on amount
Density, pressure, refractive index and surface tension are intensive (unchanged by how much material you have); volume and heat capacity are extensive (they scale with amount) — sorting a list of properties into these two buckets is really just asking whether doubling the sample doubles the property.
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- ✓ΔU_cycle = 0 for any full cycle since internal energy is a state function; entropy change for individual steps within the cycle need not be zero.
- ✓Spontaneous condensation of steam decreases the system's own entropy — it's the surroundings' larger entropy gain that makes the overall process spontaneous.
- ✓On a ΔG°=-RT ln K vs T plot, the crossing point where ln K = 0 marks where the reaction becomes spontaneous (K>1).
- ✓Intensive properties (density, pressure, refractive index, surface tension) don't scale with sample size; extensive ones (volume, heat capacity) do.
Don't assume a spontaneous process always increases the system's own entropy — spontaneity depends on the TOTAL entropy change (system + surroundings), and steam condensing is the classic counterexample where the system's entropy falls.
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