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

$V_{f}=\frac{1.5 \times 298 V_{i}}{1 \times 288}=\frac{447 }{288}V_{i = 1.55 Vi}$

The volume becomes greater by a factor of 1.55.