Question

What will happen to the volume of a bubble of air found underwater in a lake, where the temperature is $15{}^{o}C$ and the pressure is 1.5 atm, if the bubble then rises to the surface where the temperature is $25{}^{o}C$ and the pressure is 1.0 atm?

• A. Its volume will become greater by a factor of 2.4
• B. Its volume will become greater by a factor of 1.55
• C. Its volume will become greater by a factor of 1.2
• D. Its volume will become smaller by a factor of 0.80

Answer 1

Answer: (B)

$\frac{P_1{V}_i}{T_1}=\frac{P_2{V}_f}{T_2}$

$V_f=\frac{P_1{T}_2}{P_2{T}_1}.V_f$

$V_i=$ volume of water bubble under water

$V_f=$ volume of water bubble at the surface

$V_f=\frac{1.5\times 298V_i}{1\times 288}=\frac{447}{288}{V}_{i=1.55Vi}$

The volume becomes greater by a factor of 1.55.