Properties Of Matter

A small spherical monoatomic ideal gas bubble \(\left( {\gamma = {5 \over 3}} \right)\) is trapped inside a liquid of density \(\rho_1\) (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T\(_0\), the height of the liquid is H and the atmospheric pressure is P\(_0\) (Neglect surface tension)

When the gas bubble is at a height y from the bottom, its temperature is :