gen-define-entropy-and-give-one-short-worked-example-6133

Define entropy and give one short worked example.

# Entropy **Entropy (S)** is a thermodynamic quantity that measures the degree of disorder or randomness in a system. It can also be understood as the number of possible microscopic arrangements (microstates) available to a system. **Mathematical definition:** $$\Delta S = \frac{q_{rev}}{T}$$ where: - ΔS = change in entropy (J/K) - q_rev = heat transferred reversibly (J) - T = absolute temperature (K) ## Worked Example **Problem:** Calculate the entropy change when 100 g of ice at 0°C melts to water at 0°C. (Heat of fusion of ice = 334 J/g) **Solution:** 1. Calculate heat absorbed: - q = mass × heat of fusion - q = 100 g × 334 J/g = 33,400 J 2. Convert temperature to Kelvin: - T = 0°C + 273 = 273 K 3. Calculate entropy change: - ΔS = q/T = 33,400 J / 273 K - **ΔS = 122 J/K** The positive entropy change indicates increased disorder as the structured ice crystal lattice breaks down into more randomly arranged liquid water molecules.