Kinetic Theory

mole of an ideal gas at constant temperature is kept inside a cylinder of length and cross-sectional area , closed by a massless piston. The cylinder is attached to a conducting rod of length , cross-sectional area and thermal conductivity , whose other end is maintained at . The piston is moved such that heat flow through the conducting rod is constant. Find the velocity of the piston when it is at a height from the bottom of the cylinder. (Neglect any loss of heat from the system.) 

One mole of an ideal gas is taken from state A to state B by three different processes, 
(i) ACB (ii) ADB (iii) AEB as shown in the P–V diagram. The heat absorbed by the gas is 

The mass of an H₂ molecule is 3.32×10⁻²⁷ kg. If 10²³ hydrogen molecules per second strike 2 cm² of a wall at an angle of 45° with the normal while moving at a speed of 10⁵ cm/s, the pressure exerted on the wall is nearly:

0.5 mole of an ideal gas at a constant temperature of 27°C is kept inside a cylinder of length L and cross-section area A, closed by a massless piston. The cylinder is attached to a conducting rod of length L, cross-section area A/19, and thermal conductivity k, whose other end is maintained at 0°C. The piston is moved such that the rate of heat flow through the rod is constant. The constant velocity of the piston when it is at height L/2 from the bottom is