Question

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 0.487 times that of the initial number of microstates?

Answer 1

From Boltzmann formula of Entropy

S = K Ln(W)

Where S = Entropy

           K = Boltzmann constant = 1.381x10^-23 JK^-1

          W = Number microstates

This equation works only if total energy is constant which I am assuming here to solve this problem

Let initial W_i = 1 then final W_f = 0.487

Now S = K (Ln W_f - Ln W_i)

              = 1.381x10^-23(Ln(0.487) - Ln(1)

             = 1.381x10^-23(-0.71949)

             = - 9.936x10^-24 JK^-1