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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
P when the bubble is at the bottom is \( T_{0} \), the height of the liquid

W is \( H \) and the atmospheric pressure is \( p_{0} \) (Neglect surface
\( (2008,4 \mathrm{M}) \)
3.
tension)
1. As the bubble moves upwards, besides the buoyancy force
the following forces are acting on it. \( (2008,4 \mathrm{M}) \)
The buoyancy force acting on the gas bubble is (Assume \( R \) is
he universal gas constant) \( \quad(2008,4 \mathrm{M}) \)
\( \rho_{l} n \operatorname{Rg} T_{0} \frac{\left(p_{0}+\rho_{l} g H\right)^{2 / 5}}{\left(p_{0}+\rho_{l} g y\right)^{2 / 5}} \) \( \frac{\rho_{l} n R g T_{0}}{\left(p_{0}+\rho_{l} g H\right)^{2 / 5}\left[p_{0}+\rho_{l} g(H-y)\right]^{3 / 5}} \) \( \rho_{l} n \operatorname{Rg} T_{0} \frac{\left(p_{0}+\rho_{l} g H\right)^{3 / 5}}{\left(p_{0}+\rho_{l} g y\right)^{8 / 5}} \)
Physics Wally
\( \frac{\rho_{l} n R g T_{0}}{\left(p_{0}+\rho_{l} g H\right)^{3 / 5}\left[p_{0}+\rho_{l} g(H-y)\right]^{2 / 5}} \)
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