I always get confused what exactly happens when two ideal gases mix.
Consider the initial situation where two gases are in a box, separated by a rigid and adiabatic wall between them. Now when the wall between them is removed, they come to equilibrium (of course assuming the process is done quasi-statically). Initially the thermodynamic quantities of the gas be
$$ U_i,\: S_i,\:T_i,\:P_i,V_i \:\:\: \:\:\: \:\:\: \:\:\: \:\:\: \:\:\: \:\:\:i=1,2 $$ Now after the wall is removed, the condition for equilibrium is attained by the condition $$ dS = 0 $$ I am not able to apply this and find out exactly the final values of the thermodynamic quantities for an arbitrary ideal gas situation (I am not particularly able convince the situation physicaly)
(for instance if we consider and the two ideal gases to obey equation, $$ P_iV_i = c_iN_iRT_i \:\:\: \:\:\: \:\:\:i=1,2 $$ where $ c_i $ is the degrees of freedom of the gas, like $ c_i = \frac{3}{2},\:\frac{5}{2} $ for monatomic and diatomic respectively.