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.

In a cylinder filled up with ideal gas end gas and closed from both ends there is a piston of mass m and cross - sectional area S (figure).In equilibrium the piston divides the cylinder into two equal parts, each with volime V_(0) . The gas ppressure is p_(0) . The piston was slightly displaced from the equlibrium position and released.Find the oscillation frequency, assuming the prosecces in the gas to be adiabatic and the friction negligible.

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. If the piston is slightly displaced by x, the net force acting on the piston is

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

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 volume 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 ?

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 ?

A weightless piston divides a thermally insulated cylinder into two equal parts. One part contains one mole of an ideal gas with adiabatic exponent gamma , the other is evacuated. The initial gas temperature is T_0 . The piston is released and the gas fills the whole volume of the cylinder. Then the piston is slowly displaced back to the initial position. Find the increment of the internal energy and entropy of the gas was resulting from these two processes.