A 25 × 10^–3 m³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O₂ molecule ?

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol^–1 K^–1]

n moles of an ideal gas with constant volume heat capcity C_V undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$$\theta $$₂' and '$$\theta $$₁' respectively, ($$\theta $$₂ > $$\theta $$₁). The temperature at the interface is :-