A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volmek `V_0` in which an ideal gas is contained under the same pressure `p_0` and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas `eta` times compared to that of the other by slowly moving the piston ?

One mole of a certain ideal gas is contained under a weight-less piston of a vertical cylinder at a temperature T . The space over the piston opens into the atmosphere. What work has to be performed on order to increase isothermally the gas volume under the piston n times by slowly raising the piston ? The friction of the piston against the cylinder walls is negligibly small.

A heat-conducting piston can freely move inside a closed thermally insulated cylinder with an ideal gas. In equilibrium the piston divides the cylinder into two equal parts, the gas temperature being equal to T_0 . The piston is slowly displaced. Find the gas temperature as a function of the ratio eta of the volumes of the greater and smaller sections. The adiabatic exponent of the gas is equal to gamma .

(i) A conducting piston divides a closed thermally insulated cylinder into two equal parts. The piston can slide inside the cylinder without friction. The two parts of the cylinder contain equal number of moles of an ideal gas at temperature T_(0) . An external agent slowly moves the piston so as to increase the volume of one part and decrease that of the other. Write the gas temperature as a function of ratio (beta) of the volumes of the larger and the smaller parts. The adiabatic exponent of the gas is gamma . (ii) In a closed container of volume V there is a mixture of oxygen and helium gases. The total mass of gas in the container is m gram. When Q amount of heat is added to the gas mixture its temperature rises by Delta T . Calculate change in pressure of the gas.

A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area A divides the cylinder into two equal parts each with volume V_(0) and pressure P_(0) in equilibrium Assume the sepatator to move without friction. The time period of oscillation for small displacements of the piston is