Step 1: Understanding the Concept:
Entropy, denoted by the symbol \( S \), is a thermodynamic state function that represents the degree of disorder or randomness in a system.
In statistical mechanics, entropy is related to the number of microstates (\( W \)) available to a system through the Boltzmann formula:
\[ S = k \ln W \]
A system with more possible microstates (ways to arrange particles and energy) has higher entropy.
Step 2: Detailed Explanation:
Entropy is a fundamental concept in the Second Law of Thermodynamics, which states that the total entropy of an isolated system can never decrease over time; it can only remain constant or increase in spontaneous processes.
The physical state of matter significantly affects entropy:
1. Solids: Particles are in fixed positions with very low randomness. Entropy is minimum.
2. Liquids: Particles have more freedom to move, increasing disorder. Entropy is higher than solids.
3. Gases: Particles move rapidly and randomly throughout the volume. Entropy is maximum.
Hence, the order of entropy is: \( S_{gas}>S_{liquid}>S_{solid} \).
The change in entropy (\( \Delta S \)) for a reversible process is given by:
\[ \Delta S = \frac{q_{rev}}{T} \]
Where \( q_{rev} \) is the heat added reversibly and \( T \) is the absolute temperature.
Step 3: Analyzing Options:
(1) Incorrect: Entropy is directly proportional to randomness.
(2) Correct: This is the standard definition of entropy in thermodynamics.
(3) Incorrect: Entropy increases in irreversible/spontaneous processes. It is not constant.
(4) Incorrect: Gases have high positive entropy. According to the Third Law of Thermodynamics, entropy is only zero for a perfectly crystalline solid at absolute zero (0 K).
Step 4: Final Answer:
Entropy is defined as the measure of randomness or disorder of a system.