Question

Statistical entropy in thermodynamics is a measure that:

• A. Is independent of the microscopic states of a system
• B. Decreases with the number of accessible microscopic states
• C. Increases as the number of accessible microscopic states increases
• D. Is constant for all ideal gases

Hint:

Entropy increases with disorder. More microstates = more ways to arrange particles = higher entropy.

Answer 1

The Correct Option is C

Step 1: In statistical thermodynamics, entropy is understood as a measure of the number of microscopic configurations \( W \) that correspond to a thermodynamic system’s macroscopic state.
Step 2: The statistical definition of entropy is given by Boltzmann’s famous equation: \[ S = k \ln W \] where:

• \( S \) is the entropy,
• \( k \) is Boltzmann’s constant,
• \( W \) is the number of accessible microstates.

Step 3: As the number of accessible microstates increases (i.e., as the system becomes more disordered or more energy levels are populated), the entropy also increases.
Why the other options are incorrect:

• (A) Entropy is fundamentally dependent on the number of microstates.
• (B) It increases—not decreases—with more microstates.
• (D) Entropy varies with state variables and is not constant even for ideal gases.