Question

A partition divides a thermally insulated box into two compartments, each of volume V. Initially, one compartment contains n moles of an ideal gas at temperature T, and the other compartment is evacuated. We break the partition and the gas expands, filling both compartments. What is the entropy change of this free-expansion process?

Microscopically calculate the entropy change in the free expansion n moles of gas at temperature T.

Answer 1

I know that since \[\Delta U = 0\] ( because the internal energy of the ideal gas depends only on temperature. so U is constant).
\[Q = W = nRTln\frac{2V}{V} = nRT \ln 2\]
So
\[\Delta S = \frac{Q}{T} = nRln2\]

I also know that in a microscopic process is
\[\Delta S = k \ln\frac{w_2}{w_1}\]
Where w = no, of microscopic states for the given process.

After that, I'm stuck.

Answer 2

no. of**