(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.

Answer

`(i) T =T_(0) [(4 beta)/((1+beta)^(2))]^((1-gamma)/2)`
`(ii) (28Q-m R Delta T)/(38 V)`