Entropy changes in various processes are crucial to understanding the Second Law of Thermodynamics. From phase transitions to chemical reactions, entropy helps explain why some processes occur spontaneously while others don't.

By examining entropy changes in isothermal, adiabatic, reversible, and irreversible processes, we gain insight into the fundamental principles governing energy transformations and the direction of natural processes.

Entropy Changes in Processes

Entropy as a State Function

• Entropy is a state function that measures the degree of disorder or randomness in a system
• It is represented by the symbol S and has units of J/K
• Entropy is an extensive property, meaning it depends on the amount of substance present

Isothermal and Adiabatic Processes

• Isothermal processes occur at constant temperature, while adiabatic processes occur without heat transfer between the system and its surroundings
• For an isothermal process, the change in entropy (ΔS) is equal to the heat transferred (q) divided by the absolute temperature (T): $ΔS = q/T$
  • In an isothermal expansion (gas expanding in a piston), entropy increases as the system becomes more disordered due to the increased volume and decreased pressure
  • In an isothermal compression (gas being compressed in a piston), entropy decreases as the system becomes more ordered due to the decreased volume and increased pressure
• For an adiabatic process, the change in entropy is zero because there is no heat transfer (q = 0): $ΔS = 0$
  • In an adiabatic expansion (rapid expansion of a gas without heat transfer), the temperature of the system decreases, but the entropy remains constant
  • In an adiabatic compression (rapid compression of a gas without heat transfer), the temperature of the system increases, but the entropy remains constant

Entropy Changes: Reversible vs Irreversible

Reversible and Irreversible Processes

• Reversible processes are those that can be reversed without any net change in the system or its surroundings, while irreversible processes cannot be reversed without a net change in the system or its surroundings
• For a reversible process, the change in entropy of the system (ΔS_sys) is equal to the heat transferred (q_rev) divided by the absolute temperature (T): $ΔS_{sys} = q_{rev}/T$
• For an irreversible process, the change in entropy of the system (ΔS_sys) is greater than the heat transferred (q_irrev) divided by the absolute temperature (T): $ΔS_{sys} > q_{irrev}/T$

Second Law of Thermodynamics and Entropy

• The Second Law of Thermodynamics states that the total entropy of the universe (system + surroundings) always increases for an irreversible process and remains constant for a reversible process
  • In an irreversible process (heat transfer from a hot object to a cold object), the entropy of the universe increases because the entropy generated by the process is always positive
  • In a reversible process (isothermal expansion of an ideal gas), the entropy of the universe remains constant because the entropy generated by the process is zero

Entropy Changes in Reactions and Transitions

Entropy Changes in Phase Transitions

• Phase transitions, such as melting, vaporization, and sublimation, involve changes in entropy due to the rearrangement of particles in the system
  • Entropy increases during melting (solid to liquid) and vaporization (liquid to gas) because the particles become more disordered as they gain translational and rotational freedom
  • Entropy decreases during freezing (liquid to solid) and condensation (gas to liquid) because the particles become more ordered as they lose translational and rotational freedom
• The change in entropy for a phase transition can be calculated using the enthalpy of the transition (ΔH_trans) and the transition temperature (T_trans): $ΔS_{trans} = ΔH_{trans}/T_{trans}$

Entropy Changes in Chemical Reactions

• Chemical reactions involve changes in entropy due to the rearrangement of atoms and molecules in the system
  • Entropy increases during reactions that produce more moles of gas than consumed (decomposition reactions), as the particles become more disordered
  • Entropy decreases during reactions that consume more moles of gas than produced (synthesis reactions), as the particles become more ordered
• The change in entropy for a chemical reaction can be calculated using the standard molar entropies (S°) of the products and reactants: $ΔS°_{rxn} = ΣS°_{products} - ΣS°_{reactants}$
  • Standard molar entropies are tabulated values that represent the entropy of a substance at standard conditions (1 atm, 298 K)

Entropy and Spontaneity

Gibbs Free Energy and Spontaneity

• The spontaneity of a process is determined by the change in Gibbs free energy (ΔG), which is a function of the change in enthalpy (ΔH), temperature (T), and change in entropy (ΔS): $ΔG = ΔH - TΔS$
  • A process is spontaneous when ΔG < 0, non-spontaneous when ΔG > 0, and at equilibrium when ΔG = 0
• The change in entropy (ΔS) contributes to the spontaneity of a process through the -TΔS term in the Gibbs free energy equation
  • A positive change in entropy (ΔS > 0) favors spontaneity, as it makes the -TΔS term more negative and ΔG more negative
  • A negative change in entropy (ΔS < 0) opposes spontaneity, as it makes the -TΔS term more positive and ΔG more positive

Temperature Dependence of Spontaneity

• The effect of entropy change on spontaneity depends on the temperature of the system
  • At high temperatures, the -TΔS term becomes more significant, and entropy changes have a greater impact on spontaneity
  • At low temperatures, the ΔH term becomes more significant, and enthalpy changes have a greater impact on spontaneity
• The Second Law of Thermodynamics states that the entropy of the universe always increases for a spontaneous process and remains constant for a process at equilibrium
  • In a spontaneous process (ice melting at room temperature), the entropy of the system and surroundings increases, leading to an overall increase in the entropy of the universe
  • In a process at equilibrium (liquid water in a sealed container at room temperature), the entropy of the system and surroundings remains constant, and there is no net change in the entropy of the universe