A small spherical monoatomic ideal gas bubble $$\left(\lambda = \frac{5}{3}\right)$$ is trapped inside a liquid of density $$\rho_r$$ (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).