Assumptions of Kinetic Theory of Gases

Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at 0°C. Mass of a helium molecule = 6.64 × 10⁻²⁷ kg and Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹.

Figure shows a large closed cylindrical tank containing water. Initially the air trapped above the water surface has a height h₀ and pressure 2p₀ where p₀ is the atmospheric pressure. There is a hole in the wall of the tank at a depth h₁ below the top from which water comes out. A long vertical tube is connected as shown. (a) Find the height h₂ of the water in the long tube above the top initially. (b) Find the speed with which water comes out of the hole. (c) Find the height of the water in the long tube above the top when the water stops coming out of the hole.

A vessel A has volume V and a vessel B has volume 2V. Both contain some water which has a constant volume. The pressure in the space above water is p_a for vessel A and p_bfor vessel B.

Figure shows a cylindrical tube of length 30 cm which is partitioned by a tight-fitting separator. The separator is very weakly conducting and can freely slide along the tube. Ideal gases are filled in the two parts of the vessel. In the beginning, the temperatures in the parts A and B are 400 K and 100 K respectively. The separator slides to a momentary equilibrium position shown in the figure. Find the final equilibrium position of the separator, reached after a long time.

At what temperature will average kinetic energy of gas be exactly half of its value at N.T.P.?

A glass tube, sealed at both ends, is 100 cm long. It lies horizontally with the middle 10 cm containing mercury. The two ends of the tube contain air at 27°C and at a pressure 76 cm of mercury. The air column on one side is maintained at 0°C and the other side is maintained at 127°C. Calculate the length of the air column on the cooler side. Neglect the changes in the volume of mercury and of the glass.

There is some liquid in a closed bottle. The amount of liquid is continuously decreasing. The vapour in the remaining part

State any four assumptions of kinetic theory of gases.