QJEEAdv08Phcef4: JEE Advanced 2008 Physics - Class 11 JEEAdv08Phcef4 Solution: When the gas bubble is at a height y from the bottom, its…

Question

Verified Solution • 2025–26 Session moderate

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

A ${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{2 \over 5}}}$
B ${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{2 \over 5}}}$
C ${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{3 \over 5}}}$
D ${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{3 \over 5}}}$

Accepted Answer

Since the process is adiabatic,

$P{V^\gamma }$ = constant for gas inside bubble.

Thus, $P{V^{(1 - \gamma )}}.\,{T^\gamma } =$ constant

$\Rightarrow {P^{1 - \gamma }}_{bottom}{T^\gamma }_{bottom} = P_y^{1 - \gamma }T_y^\gamma =$ constant

$\Rightarrow {({P_0} + {\rho _1}gH)^{ - 2/3}}(T_0^{5/3}) = ({P_0} + {\rho _1}g{(H - y)^{ - 2/3}}){T^{5/3}}$

$\Rightarrow {T_0} = {\left[ {{{{P_0} + {\rho _1}g(H - y)} \over {{P_0} + {\rho _1}gH}}} \right]^{2/5}}$

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