Question

We have a system A with 8 particles and a total energy of 4 units. Each particle is allowed to have an energy of either 0 or 1 units only. What is the multiplcity of this system W? What is the value of S/kB= lnW?

Answer 1

We have system A with 8 particles and total energy of 4 units, the multiplicity W for the system is given by

W= 8!/ 4! 4!

W= 8×7×6×5×4×3×2×1/ (4×3×2×1)(4×3×2×1)

By simple multiplication and division we get,

W= 70 ( By factorial method)

lnW = ln(70) = 4.2484 .

To find out value of S/kB= lnW,

We have entropy equation S=kB(lnW)

Where S= Entropy of the system

kB= Boltzmann's constant which is 1.38×10^-23 JK^-1

W= Number of ways of arranging particles that give rise to a particular observed state of the system.

We have given values ,

kB=1.38×10^-23JK^-1 and lnW= 4.2484

Applying in the equation,

S=kB(lnW)

S= 1.38×10^-23JK^-1× 4.2484

S= 5.862×10^-23JK^-1

The unit of entropy is Joule per kelvin (J/K or JK^-1)