Question #158093

Calculate the entropy of a system having 6.9×10^10 microstates


1
Expert's answer
2021-01-27T04:36:03-0500

Ludwig Boltzmann developed a molecular-scale statistical model that related the entropy of a system to the number of microstates possible for the system. A microstate (W) is a specific configuration of the locations and energies of the atoms or molecules that comprise a system like the following:


S=k lnWS = k \ ln W

Here k is the Boltzmann constant and has a value of 1.38×1023J/K1.38 × 10^{−23} J/K .


S=1.38×1023×ln W=1.38×1023×ln (6.9×1010)=1.38×1023×24.96=3.44×1022 J/K\begin{aligned}S &= 1.38× 10^{-23} × \ln \ W\\ &= 1.38 × 10^{-23} × \ln\ (6.9×10^{10})\\ &= 1.38 × 10^{-23} × 24.96\\ &= 3.44 × 10^{-22} \ J/K \end{aligned}


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