Entropy (S) | Thermodynamics Class 11

Entropy ($S$)

Measure of Randomness & Disorder | Thermodynamics

1. What is Entropy?

Definition: Entropy ($S$) is a thermodynamic state function that measures the degree of randomness or disorder in a system.

The greater the disorder, the higher the entropy. The natural tendency of the universe is to move towards maximum disorder.

Order of Entropy: $\text{Gas} \gg \text{Liquid} > \text{Solid}$

2. Mathematical Formulation

Entropy change is related to the heat exchanged in a reversible process.

$$ \Delta S = \frac{q_{rev}}{T} $$

• $\Delta S$ = Change in Entropy
• $q_{rev}$ = Heat absorbed reversibly
• $T$ = Temperature in Kelvin

Unit: $J \cdot K^{-1} \cdot mol^{-1}$ (or Entropy Unit, e.u.)

3. Factors Affecting Entropy

• Physical State: Gas > Liquid > Solid. (e.g., $H_2O(s) \to H_2O(l)$, $\Delta S > 0$).
• Temperature: As T increases, kinetic energy and disorder increase $\Rightarrow S$ increases.
• Pressure/Volume: For gases, expansion (Volume $\uparrow$, Pressure $\downarrow$) increases randomness $\Rightarrow S$ increases.
• Mixing: Mixing of gases or forming a solution increases disorder $\Rightarrow \Delta S_{mix} > 0$.

4. Predicting Sign of $\Delta S$ in Reactions

For a chemical reaction, check the change in the number of gaseous moles ($\Delta n_g$).

• If $\Delta n_g > 0$ (More gas produced): $\Delta S$ is Positive.
• If $\Delta n_g < 0$ (Gas consumed): $\Delta S$ is Negative.
• If $\Delta n_g = 0$: $\Delta S$ is small (check structure complexity).

Example: $N_2(g) + 3H_2(g) \to 2NH_3(g)$.
$\Delta n_g = 2 - 4 = -2$. Randomness decreases. $\Delta S < 0$.

5. Second Law of Thermodynamics

Statement: For any spontaneous (irreversible) process, the total entropy of the universe (System + Surroundings) always increases.

$$ \Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} > 0 $$

• $\Delta S_{total} > 0$: Spontaneous
• $\Delta S_{total} = 0$: Equilibrium
• $\Delta S_{total} < 0$: Non-spontaneous

6. Relation to Gibbs Energy

Entropy is a key component of Gibbs Free Energy ($G$), which determines spontaneity at constant T and P.

$$ \Delta G = \Delta H - T\Delta S $$

To make $\Delta G$ negative (spontaneous), a positive $\Delta S$ (disorder) helps, especially at high temperatures.

Practice Quiz

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