What is the entropy of a closed system in which 25 distinguishable grains of sand are distributed among 1000 distinguishable equ alsized compartments with only one grain per compartment?
2 answers:
Answer:
S = 172.69 J/K
Explanation:
For a closed system, the entropy is given as the natural logarithm of microstates.
The number of particles (grains of sand); N = 25
The number of boxes (compartments); M = 1000
Entropy is the logarithm of number of microstates; Thus,
S = In ψ
However, the number of microstates is given by the formula;
ψ = Mⁿ
Thus, S = In Mⁿ
Plugging in the relevant values to obtain;
S = In (1000)^(25)
S = 172.69 J/K
Answer:
The entropy of the closed system is
S = (1.58 × 10⁻²¹) J/K
Explanation:
Entropy of a system is proportional to the number of different microstates. The constant of proportionality is the Boltzmann's constant.
S = K In W
K = Boltzmann's constant = (1.381 × 10⁻²³) J/K.
Number of different microstates possible for distributing 25 distinguishable grains of sand among 1000 distinguishable equal sized compartments with only one grain per compartment = ¹⁰⁰C₂₅ = (4.7642 × 10⁴⁹)
S = (1.381 × 10⁻²³) In (4.7642 × 10⁴⁹)
S = 1.381 × 10⁻²³ × 114.4
S = (1.58 × 10⁻²¹) J/K
Hope this Helps!!!
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