[QUE/TH-08004] TH-PROBLEM

Consider a system consisting of $N_1$ atoms of Neon gas, of mass $m_1$ and $N_2$ atoms of Argon gas of mass $m_2$ are in a box a volume $V$. The system is in thermal equilibrium at temperature $T$. Treating them as ideal gas, find the entropy $S$  and the Gibbs free energy $G$ of the system.[ Assume the arbitrary solution of Gibb for the resoultion of the Gibbs paradox]. Answer to be in terms of $N_1\,,\,N_2\,,\,m_1\,,\,m_2\,,\,T$ and the fundamental concepts $h$ and $k$