$20-35.$ We can use the equation $S=klnW$ to derive Equation $20\mathrm{.}28.$ First, argue that the probability that an ideal$-$gas molecule is found in a subvolume $V_s$ of some larger volume $V$ is $\frac{V_s}{V}.$ Because the molecules of an ideal gas are independent, the probability that

$850$

Chapter $20/$ Entropy and the Second Law of Thermodynamic

$N$ ideal$-$gas molecules are found in $V_s$ is $(\frac{V_s}{V}{)}^N.$ Now show that the change in entropy when the volume of one mole of an ideal gas changes isothermally from $V_1$ to $V_2$ is

$S=Rln\frac{V_2}{V_1}$