Question

Which of the following is true for entropy?

• A. Entropy decreases with increase in randomness
• B. Entropy is the measure of randomness of a system
• C. Entropy remains constant in every process
• D. Entropy is always zero for gases

Hint:

Remember the entropy order: \[ \text{Solid} < \text{Liquid} < \text{Gas} \] More freedom of movement \(\Rightarrow\) More randomness \(\Rightarrow\) Higher entropy. Also:
• Melting increases entropy
• Vaporization greatly increases entropy
• Cooling decreases entropy

Answer 1

The Correct Option is B

Concept: Entropy is a thermodynamic quantity that measures the degree of randomness, disorder, or molecular chaos present in a system. It is represented by the symbol: \[ S \] A system with greater randomness possesses higher entropy. Examples: \[ \text{Solid} < \text{Liquid} < \text{Gas} \] because gaseous particles move more freely and randomly than liquids and solids.

Step 1: Understanding the meaning of entropy.
Entropy tells us how disordered a system is.
• Highly ordered systems \(\rightarrow\) Low entropy
• Highly random systems \(\rightarrow\) High entropy For example:
• Ice has lower entropy because molecules are arranged systematically.
• Water vapor has very high entropy because molecules move randomly in all directions.

Step 2: Analyzing each given option.

• Entropy decreases with increase in randomness: Incorrect because entropy actually increases with randomness.
• Entropy is the measure of randomness of a system: Correct statement.
• Entropy remains constant in every process: Incorrect because entropy changes during physical and chemical processes.
• Entropy is always zero for gases: Incorrect. Gases generally possess very high entropy.

Step 3: Important thermodynamic interpretation.
Entropy change is given by: \[ \Delta S = \frac{q_{rev}}{T} \] where:
• \(\Delta S\) = change in entropy
• \(q_{rev}\) = reversible heat exchanged
• \(T\) = absolute temperature Entropy tends to increase naturally in spontaneous processes.

Step 4: Final conclusion.
Therefore, the correct statement regarding entropy is: \[ \boxed{\text{Entropy is the measure of randomness of a system}} \] Hence, the correct option is: \[ \boxed{(2)\ \text{Entropy is the measure of randomness of a system}} \]