Question

Assume you have a system that can have one of six distinct energy states E1 E2 E3 E4 E5 E6 what is the entropy of an ensemble of five systems where one system is in energy state E2 three systems are in energy state E3 and one system is in energy state E6.

Choose the correct answer

S= Kb ln(120)

S= Kb ln(24)

S= Kb ln(20)

S= Kb ln(5)

S= Kb ln(2)

S=0

Answer 1

Answer: Entropy of the assembly will be

S = kb ln (W)..............(1)

Where W is thermodynamic probability of the assembly.

By the given question, one system is in E2 state, three systems are in E3 energy state and one system is in E6 state.

Therefore, thermodynamic probability

=

Or

Or

W = 20

Substituting in equation (1)

S = kb ln (20)

Therefore (C)part correct option