A small spherical monoatomic ideal gas bubble ( = 5 3 ) is trapped inside a liquid of…

A small spherical monoatomic ideal gas bubble \(\left(\gamma=\frac{5}{3}\right)\) is trapped inside a liquid of density r_l (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 T₀, the height of the liquid is H and the atmospheric pressure is P₀ (neglect surface tension).

The buoyancy force acting on the gas bubble is (assume R is the universal gas constant).