Answer to Question #158093 in Organic Chemistry for Priya

Question

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

Answer 1

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:

$S = k \ ln W$

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

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