List of top Nano Technology Questions on Entropy asked in AP PGECET

According to the Boltzmann Equation $S = k_B \ln \Omega$, if a system is in a state of "Perfect Order" (a perfect crystal at $0\text{ K}$), the number of microstates $\Omega$ and the entropy $S$ are

The Third Law of thermodynamics states that entropy at absolute zero is:

Stirling's approximation is used to simplify:

In statistical thermodynamics, Stirling's Approximation ($\ln N! \approx N \ln N - N$) is valid only when

Mixing identical gases results in

Calculate the increase in entropy when two identical containers, each containing 1 mole of an ideal gas at 300 K and 1 atm, are allowed to mix freely.
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During an isothermal expansion of an ideal gas, how does the entropy of the system change?

What does the Third Law of Thermodynamics state about the entropy of a perfect crystal at absolute zero temperature?

Consider a process where the entropy change of the system is negative. What can be inferred if the process is spontaneous?