# Determining an expression for an entropy equation

by Benzoate
Tags: determining, entropy, equation, expression
 Sci Advisor HW Helper PF Gold P: 2,532 You can't apply $\Delta S_A=Nk\ln 2$ to the general problem; that's the increase in entropy for a single gas expanding into twice its original volume. If $x$ can vary, there's no reason to assume the volume doubles. Also, remember that as $x$ increases, there are no longer $N$ molecules of gas A but rather $(1-x)N$. One common way to show your desired relation is to assume that each gas expands from its original volume into the total volume and to use the Maxwell relation $$\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V=\frac{nR}{V}\quad$$ $$dS=\frac{nR}{V}\,dV$$ to calculate the change in entropy.