A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.842 times that of the initial number of microstates

Answer: - 2.373 x 10^-24J/K (particles

Explanation: Entropy is defined as the degree of randomness of a system which is a function of the state of a system and depends on the number of the random microstates present.

The entropy change for a particle in a system depends on the initial and final states of a system and is given by Boltzmann equation as

S = k ln (W).

where S = Entropy

K IS Boltzmann constant = =1.38 x 10 ^-23J/K

W is the number of microstates available to the system.

The change in entropy is given as

S2 - S1 = kln W2 - klnW1

dS = k ln (W2/W1)

where w1 and w2 are initial and final microstates

from the question, W2 (final) = 0.842 x W1 (initial), so:

= 1.38*10-23 ln (0.842)

=1.38*10-23 x - 0.1719

= - 2.373 x 10^-24J/K (particles)