QJEEAdv08Ph5cf4: JEE Advanced 2008 Physics - Class 11 JEEAdv08Ph5cf4 Solution: The buoyancy force acting on the gas bubble is (Assume R is the …

Buoyancy force = Weight of fluid displaced

= (mass of fluid displaced)g

$= V{\rho _l}g$ .... (i)

Where V = Volume of fluid displaced

= Volume of the bubble

$PV = nRT$

$\Rightarrow V = {{nRT} \over P} = {{nRT} \over {{P_0}(H - y){\rho _l}g}}$ .... (ii)

Where P is the pressure of the bubble at an arbitrary location at a distance 'y' from the bottom.

Put the value of temperature from eq. (i)

$V = {{nR} \over {[{P_0} + (H - y){\rho _l}g]}} \times {{{T_0}{{[{P_0} + (H - y){\rho _l}g]}^{2/5}}} \over {{{[{P_0} + H{\rho _l}g]}^{2/5}}}}$

$= {{nR{T_0}} \over {{{[{P_0} + (H - y){\rho _l}g]}^{3/5}}{{[{P_0} + H{\rho _l}g]}^{2/5}}}}$ .... (iii)

From eq. (i) and (iii) Buoyance force

$= {{nR{T_0}{\rho _1}g} \over {{{[{P_0} + (H - y){\rho _l}g]}^{3/5}}{{[{P_0} + H{\rho _l}g]}^{2/5}}}}$