Why is entropy positive when a solid becomes a gas

Entropy measures the number of microscopic ways a system can arrange its energy. In a solid, atoms vibrate around fixed lattice points, giving few configurations. In a gas, molecules move freely in three dimensions, rotate, and translate, creating vastly more microstates. The statistical definition $S = k_B \ln \Omega$ shows that a larger $\Omega$ yields higher entropy, so the transition solid → gas raises $S$. The increase in positional disorder also raises the probability of any particular arrangement, further enlarging $\Omega$.

Quantitative example: dry‑ice sublimation

From the thermodynamic side, the entropy change for a reversible phase change at constant pressure is given by $\Delta S = \frac{\Delta H_{\text{trans}}}{T}$. The enthalpy of sublimation is positive because energy is required to break the solid lattice, and dividing by the absolute temperature yields a positive ΔS. This formula matches the statistical picture: more energy input creates more ways to distribute it among gas molecules.

Compute ΔS for CO₂ sublimation at 1 atm

1. 1Find ΔH_sub (≈ 25.2 kJ mol⁻¹).
2. 2Use the temperature of sublimation (≈ 194 K).
3. 3Apply ΔS = ΔH_sub / T.

Values used in the calculation

Why entropy rises

• Huge increase in accessible volume
• Addition of translational and rotational degrees of freedom
• Breakdown of ordered lattice into random positions

Because ΔS is positive, the Gibbs free energy change $\Delta G = \Delta H - T\Delta S$ can become negative at temperatures above the sublimation point, making the process spontaneous. This explains why solids such as dry ice readily turn into gas when heated.