Question

The second law of thermodynamics defines entropy(S), a state function? Which of the following statement is valid for entropy of an isolated system.

• A. For an isolated system at equilibrium, both energy and disorder are fixed.
• B. Foran isolated system undergoing a spontaneous change, entropy decreases.
• C. For an isolated system undergoing a spontaneous change, both energy and entropy increases.
• D. For an isolated system undergoing spontaneous change, entropy can never decrease.

Answer 1

Answer: (D)

D

Answer 2

The question asks to identify the valid statement regarding the entropy of an isolated system based on the Second Law of Thermodynamics.

Let's analyze each option:

• Second Law of Thermodynamics for Isolated Systems: The Second Law states that for any spontaneous (irreversible) process occurring in an isolated system, the entropy of the system always increases ($\Delta S_{isolated} > 0$). For a reversible process or when the system is at equilibrium, the entropy of the isolated system remains constant ($\Delta S_{isolated} = 0$). Combining these, the entropy of an isolated system can never decrease ($\Delta S_{isolated} \ge 0$).

• Isolated System: An isolated system is one that cannot exchange energy (heat or work) or matter with its surroundings. According to the First Law of Thermodynamics, the total energy of an isolated system remains constant.

Now let's evaluate the given options:

• (A) For an isolated system at equilibrium, both energy and disorder are fixed.

  • Energy: For any isolated system (whether at equilibrium or undergoing change), its total energy is conserved and thus fixed (First Law of Thermodynamics).
  • Disorder (Entropy): At equilibrium, an isolated system reaches its state of maximum entropy. Therefore, at equilibrium, the entropy (disorder) is fixed and at its maximum value.
  • This statement is correct for an isolated system at equilibrium.

• (B) For an isolated system undergoing a spontaneous change, entropy decreases.

  • This contradicts the Second Law of Thermodynamics. For a spontaneous change in an isolated system, entropy increases ($\Delta S_{isolated} > 0$).
  • Therefore, this statement is incorrect.

• (C) For an isolated system undergoing a spontaneous change, both energy and entropy increases.

  • Energy: For an isolated system, energy is conserved and remains constant; it does not increase.
  • Entropy: For a spontaneous change, entropy does increase.
  • Since energy does not increase, this statement is incorrect.

• (D) For an isolated system undergoing spontaneous change, entropy can never decrease.

  • For a spontaneous change in an isolated system, entropy increases ($\Delta S_{isolated} > 0$). If entropy is increasing, it certainly "can never decrease".
  • More broadly, the Second Law states that the entropy of an isolated system never decreases. It either increases (for spontaneous/irreversible processes) or remains constant (for reversible processes or at equilibrium).
  • This statement accurately reflects the fundamental principle of the Second Law of Thermodynamics for isolated systems. It encompasses the condition for spontaneity and the condition for equilibrium.

Comparing (A) and (D): Option (A) is a correct statement about the state of an isolated system at equilibrium. Option (D) is a more general and fundamental statement derived from the Second Law of Thermodynamics, applicable to the overall behavior of entropy in an isolated system, including during spontaneous changes and at equilibrium. The phrase "can never decrease" directly translates to $\Delta S_{isolated} \ge 0$, which is the mathematical expression of the Second Law for isolated systems.

Therefore, option (D) is the most comprehensive and accurate statement describing the behavior of entropy for an isolated system.

Explanation of the solution: The Second Law of Thermodynamics states that the entropy of an isolated system either increases (for spontaneous processes) or remains constant (at equilibrium/reversible processes), but it never decreases. Option (D) directly reflects this fundamental principle by stating that for an isolated system undergoing spontaneous change, entropy can never decrease, which is true as entropy must increase or stay constant. Options (B) and (C) are incorrect as they contradict the Second Law regarding entropy change or the First Law regarding energy conservation in an isolated system. Option (A) is true for equilibrium, but (D) provides a more general and encompassing statement about the entropy of an isolated system.