Question

A bubble of air is underwater at temperature $15^{\circ}C$ and the pressure $1.5$ bar. If the bubble rises to the surface where the temperature is $25^{\circ}C$ and the pressure is$ 1.0$ bar, what will happen to the volume of the bubble ?

• A. Volume will become greater by a factor of 1.6
• B. Volume will become greater by a factor of 1.1
• C. Volume will become smaller by a factor of 0.70
• D. Volume will become greater by a factor of 2.9

Answer 1

Answer: (A)

$\because \frac{p_{1} V_{1}}{T_{1}}=\frac{p_{2} V_{2}}{T_{2}}$ (By ideal gas equation)
or $\frac{1.5 \times V_{1}}{288}=\frac{1 \times V_{2}}{298}$
$V_{2}=1.55\, V_{1}$
i.e., volume of bubble will be almost $1.6$ times to initial volume of bubble.