Question

what is the entropy of a closed system in which 20 distinguishable grains of sand are distributed among 1000 distinguishable equal-sized compartments?

Answer 1

The entropy of a closed system is 138.16 J/K

How to calculate the entropy of a closed system

For a closed system, the entropy is given as the natural logarithm of microstates.

The number of distinguishable grains of sand, N = 20

The number of distinguishable equal-sized compartments, M = 1000

Entropy is the logarithm of the number of micro-states. So, the entropy, S = In ψ

However, the number of micro-states is given by the formula; ψ = Mⁿ

So, S = In Mⁿ

Inputting the necessary values to get the value;

S = In (1000)^(20)

S = 138.16 J/K