Paragraph: A small spherical monoatomic ideal gas bubble ( γ = 3 5 ) is trapped inside a liquid of density ρ 1 (see figure). Assume that the bubble does not exchange any heat with the liquid. The

Question

Paragraph: A small spherical monoatomic ideal gas bubble ( γ = 3 5 ​ ) is trapped inside a liquid of density ρ 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). Question: The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

TestHub · Accepted Answer

Buoyancy force Here, and F T 2 ​ p 2 ​ ​ = ( volume of bubble ) ( ρ l ​ ) g = ( p 2 ​ n R T 2 ​ ​ ) p l ​ g = T 0 ​ [ p 0 ​ + ρ l ​ g H p 0 ​ + p l ​ g ( H − y ) ​ ] = p 0 ​ + p l ​ ( H − y ) ​ Substituting the values we get, F = ( p 0 ​ + ρ l ​ g H ) 2/5 [ p 0 ​ + ρ l ​ g ( H − y ) ] 3/5 ρ n ​ n g T 0 ​ ​ ∴ correct option is (b).

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