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A small spherical monoatomic ideal gas double  is trapped inside a liquid of density 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 T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).
[JEE 2008]
Figure :                                                                                                                   
                   
  • a)
     
  • b)
     
  • c)
     
  • d)
     
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A small spherical monoatomic ideal gas doubleis trapped inside a liqui...
Since the process is adiabatic,
PVγ=constant for gas inside bubble.
Thus P1−γTγ=constant
Pbottom1−γ​Tbottomγ​= Py1−γ​Tyγ​=constant
⟹(P0​+ρ1​gH)−2/3(T0​)5/3=(P0​+ρ1​g(H−y)−2/3)T5/3
⟹T=T0​(P0​+ρ1​g(H−y)/ P0​+ρ1​gH​)2/3
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A small spherical monoatomic ideal gas doubleis trapped inside a liqui...
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A small spherical monoatomic ideal gas doubleis trapped inside a liquid of density 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 T0, the height of the liquid is H and the atmospheric pressure is P0(Neglect surface tension).[JEE 2008]Figure : a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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