Question

An underwater bubble with radius 0.5cm at the bottom of the tank, where the temperature is 5 c and pressure is 3 atm rises to the surface where the temperature is 25 c. the vapor pressure and the pressure is 1 atm. What will be the radius of the bubble when it reaches the surface?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{The}\mathrm{moles}\mathrm{of}\mathrm{air}\mathrm{contained}\mathrm{in}\mathrm{bubble}\mathrm{at}\mathrm{the}\mathrm{bottom}\mathrm{of}\mathrm{tank}\mathrm{as}\mathrm{well}\mathrm{as}\mathrm{on}\mathrm{the}\mathrm{surface}\mathrm{remains}\mathrm{same}. \\ \mathrm{Thus},\mathrm{n}=\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{RT}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{RT}}_2} \\ \mathrm{moles}\mathrm{at}\mathrm{the}\mathrm{bottom}\mathrm{of}\mathrm{the}\mathrm{tank}=\mathrm{moles}\mathrm{at}\mathrm{the}\mathrm{surface} \\ \mathrm{or},\frac{3\times \left({\displaystyle \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\mathrm{\pi }\times (0.5{)}^3}{\mathrm{R}\times 278}=\frac{1\times \left({\displaystyle \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right){\mathrm{\pi r}}^3}{\mathrm{R}\times 298} \\ \mathrm{or},\mathrm{r}=0.74\mathrm{cm} \end{gathered}$$

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