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.

A masslesss piston divides a closed thermallyy insulated cylinder into two equal parts. One part contains M = 28 g of nitrogen. At this temperature, one-third of molecules are dissociated into atoms and the other part is evacuated. The piston is released and the gas fills the whole volume of the cylinder at temperature T_(0) . Then, the piston is slowly displaced back to its initial position. calculate the increases in internal energy of the gas. Neglect further dissociation of molecules during, the motion of the piston.

A masslesss piston divides a closed thermallyy insulated cylinder into two equal parts. One part contains M = 28 g of nitrogen. At this temperature, one-third of molecules are dissociated into atoms and the other part is evacuated. The piston is released and the gas fills the whole volume of the cylinder at temperature T_(0) . Then, the piston is slowly displaced back to its initial position. calculate the increases in internal energy of the gas. Neglect further dissociation of molecules during, the motion of the piston.

A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V. 2 moles of an ideal gas at pressure P = 2 atmosphere are confined to the part with volume V =1 litre. The remainder of the cylinder is evacuated. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heats of the gas, gamma =1.5 .

A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V.2 moles of an ideal gas at pressure P = 2 atmosphere are confined to the part with volume V =1 litre. The remainder of the cylinder is evacuated. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heats of the gas, gamma =1.5 .

A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V.2 moles of an ideal gas at pressure P = 2 atmosphere are confined to the part with volume V =1 litre. The remainder of the cylinder is evacuated. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heats of the gas, gamma =1.5 .

A mass less piston divides a thermally insulated cylinder into two parts having volumes V = 2.5 litre and 3 V = 7.5 litre. 0.1 mole of an ideal gas is confined into the part with volume V at a pressure of P = 10^(5) N//m^(2) . The other part of the cylinder is empty. The piston is now released and the gas expands to occupy the entire volume of the cylinder. Now the piston is pressed back to its initial position. Find final temperature of the gas. [Take R = (25)/(3) J mol^(-1) K^(-1) and gamma = 1.5 for the gas]

(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 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 .