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A small spherical monoatomic ideal gas b...

A small spherical monoatomic ideal gas bubble `(gamma = 5/3)` is trapped inside a liquid of density `rho_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 `T_0` the height of the liquid is H and the atmospheric pressure is `P_0` (Neglect surface tension).

When the gas bubble is at a height y from the bottom, its temperature is :

A

`T_(0) ( (p_0 + rho_(1) gH)/( p_(0) +rho_(1) gy) )^(2//5)`

B

`T_(0) ((p_(0) + rho_(1) g(H-y) )/( p_(0) + rho_(1) gH) )^(2//5)`

C

`T_0 ((p_(0) + rho_(1) gH)/( p_(0) +rho_(1) gH) )^(3//5)`

D

`T_0 ((p_(0) + rho_(1)g(H-y) )/( p_(0) +rho_(1) gH) )^(3//5)`

Text Solution

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The correct Answer is:
B
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