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 :

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

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

Calculate the value of mean free path ($$\lambda$$) for oxygen molecules at temperature 27$$^\circ$$C and pressure 1.01 $$\times$$ 10⁵ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 $$\times$$ 10^$$-$$23 JK^$$-$$1)