A system has 4 accessible microstates. Using S = k ln W with k = 1.381 × 10⁻²³ J/K, compute its entropy in units of 10⁻²³ J/K, to two decimal places.

Chemistry I / Entropy and the Second Law

Practice question · Numerical answer

A system has 4 accessible microstates. Using $S = k \ln W$ with $k = 1.381 \times 10^{-23}$ J/K, compute its entropy in units of $10^{-23}$ J/K, to two decimal places.

Hints

Take the natural logarithm of the number of microstates, then multiply by k.
ln 4 = 1.386, so compute 1.381 x 1.386.

Show the answer

1.91 (answers within ±0.04 count)

Why

$S = k\ln W = 1.381 \times 10^{-23} \times \ln 4 = 1.381 \times 1.386 = 1.91 \times 10^{-23}$ J/K. Entropy grows only logarithmically, so doubling the microstate count adds a fixed amount rather than doubling $S$ .

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A system has 4 accessible microstates. Using S=kln⁡WS = k \ln WS=klnW with k=1.381×10−23k = 1.381 \times 10^{-23}k=1.381×10−23 J/K, compute its entropy in units of 10−2310^{-23}10−23 J/K, to two decimal places.

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A system has 4 accessible microstates. Using $S = k \ln W$ with $k = 1.381 \times 10^{-23}$ J/K, compute its entropy in units of $10^{-23}$ J/K, to two decimal places.