Twenty-five identical molecules are in a box.Microstates are designated by identifying the molecules in the left and right halves of the box.The Boltzmann constant is 1.38 *10^-23 J/K.The entropy associated with the configuration for which 15 molecules are in the left half and 10 molecules are in the right half is: A)2.07 * 10^-22 J/K B)7.31 *10^-22 J/K C)4.44 * 10^-23 J/K D)6.91 *10^-23 J/K E)2.22 * 10^-23 J/K

Question

Quizplus · Accepted Answer

The entropy associated with the configuration for which 15 molecules are in the left half and 10 molecules are in the right half is given by:S = k * ln(W)where k is the Boltzmann constant and W is the number of microstates.In this case, there are 25! ways to distribute the molecules in the box, and 15! ways to distribute the molecules in the left half of the box. Therefore, the number of microstates is:W = 25! / (15! * 10!) = 3003Substituting this into the equation for entropy, we get:S = 1.38 * 10^-23 J/K * ln(3003) = 2.07 * 10^-22 J/KTherefore, the correct answer is A.

Twenty-Five Identical Molecules Are in a Box