A polyatomic ideal gas has 24 vibrational modes. What is the value of $$\gamma$$?

Two ideal polyatomic gases at temperatures T₁ and T₂ are mixed so that there is no loss of energy. If F₁ and F₂, m₁ and m₂, n₁ and n₂ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :

If an electron is moving in the n^th orbit of the hydrogen atom, then its velocity (v_n) for the n^th orbit is given as :

Two identical metal wires of thermal conductivities K₁ and K₂ respectively are connected in series. The effective thermal conductivity of the combination is :