Thermal Physics - Entropy

Questions 71-73

A system in thermal equilibrium at temperature T consists of a large number N₀ of subsystems, each of which can exist only in two states of energy E₁ and E₂, where . In the expressions that follow, k is the Boltzmann constant.

Which of the following is true of entropy of the systems?

A. It increases without limit with T from zero at T = 0
B. It decreases with increasing T
C. It increases from zero at T = 0 to N₀k ln 2 at arbitrarily high temperature
D. It is given by N₀k [⁵/₂ ln T − ln p + constant]
E. It cannot be calculated from the information given

(GR9277 #73)

Solution:

At low T, entropy S(T → 0) = 0
At high T, S = kσ

σ = ln (number of states with the same total energy)

For 2  states of energy, σ = ln 2
S = k ln 2

For N₀ subsystems.
S = N₀k ln 2

Answer: C