JEE Advanced2008PhysicsMechanical Properties of FluidsActual
Paragraph: A small spherical monoatomic ideal gas bubble ( = 5 3 ) is trapped inside a liquid of density 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 T₀ , the height of the liquid is H and the atmospheric pressure is p₀ (Neglect surface tension). Question: When the gas bubble is at
Options
- AT₀ ( p₀+ H p₀+ y )^ 2 5
- BT₀ ( p₀+ l g(H-y) p₀+ l g H )^ 2 5
- CT₀ ( p₀+ l g H p₀+ y )^ 3 5
- DT₀ ( p₀+ l g(H-y) p₀+ l g H )^ 3 5
Correct answer
B. T₀ ( p₀+ l g(H-y) p₀+ l g H )^ 2 5
Step-by-step solution
As there is no exchange of heat. Therefore, process is adiabatic. Applying, array rlrl & T p^ 1- = constant & T₂ p₂^ 1- =T₁ p₁^ 1- or & T₂ & =T₁ ( p₁ p₂ )^ 1- =T₁ ( p₂ p₁ )^ -1 array Substituting the values we have, aligned T₂ & =T₀ [ p₀+ (H-y)^T p₀+ H ]^ 5 / 3-1 5 / 3 & =T₀ [ p₀+ (H-y) p₀+ H ]^ 2 / 5 aligned correct option is (b).