Assumptions of Kinetic Theory of Gases

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.

Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel

The quantity \[\frac{pV}{kT}\] represents

State any four assumptions of kinetic theory of gases.

Prove that root mean square velocity of gas molecule is directly proportional to the square root of its absolute temperature.

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.

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.

If the mass of all molecules of a gas is halved and their speeds doubled, then the ratio of initial and final pressures is ________.