A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{3}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (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 $\mathrm{T}_0$, the height of the liquid is H and the atmospheric pressure is $\mathrm{P}_0$ (Neglect surface tension).
The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
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