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Earth's atmosphere is a layer of gases that surround it, permitting life and protecting life by absorbing ultraviolet solar radiation, warming the surface by retaining the heat and mitigating the temperature difference between day and night.

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volume of the air bubble in the water

Using the ideal gas law: $P(h) = P_0 + \rho_w g h$, ${V_o P_0} = {V(h) P(h)}$ which gives $V(h) = {V_o P_0}{1 \over P_0 + \rho_w g h}$.
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