Thermal Physics - Entropy

A sealed and thermally insulated container of total volume V is divided into two equal volumes by an impermeable wall. The left half of the container is initially occupied by n moles of a ideal gas at temperature T. Which of the following gives the change in entropy of the system when the wall is suddenly removed and the gas expands to fill the entire volume?

A. 2nR ln 2
B. nR ln 2
C. ½nR ln 2
D. -nR ln 2
E. -2nR ln 2

(GR0177 #47)

Solution:

The container is thermally insulated, dT = 0 or T constant → Isothermal expansion

Entropy for Isothermal expansion: S = Nk ln (V_f / V_i )

Since V_f = 2V_i → S = Nk ln 2 = nR ln 2

Answer: B