KVPY Sample Paper KVPY Stream-SX Model Paper-20

A system consists of three coins that can come up either head or tail. Coins are tossed and that results in two tails and one head. Entropy of three coins system will be

A) \[\frac{{{k}_{B}}}{3}\]

B) \[3{{k}_{B}}\]

C) \[\frac{{{k}_{B}}}{\ln 3}\]

D) \[{{k}_{B}}\cdot \ln 3\]

Correct Answer: D

Solution :

We use Boltzmann relation

\[S={{k}_{B}}\cdot \ln \Omega \], where \[\Omega \] is the number of ways the state can occur.

Here two tails and one head can occur in three different ways.

So, entropy, \[S={{k}_{B}}\cdot \ln 3\]