Question

A bubble of air is underwater at temperature 15 ${}^{o}C$ and the pressure 1.5 bar. If the bubble rises to the surface where the temperature is 25 ${}^{o}C$ 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 2.5

Answer 1

The correct option is A Volume will become greater by a factor of 1.6

The pressure, temperature and volume under two different sets of conditions ar related by the following expression.

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$......(1)

Let $V$ be the initial volume. Substitute values in the above expression.

$\frac{1.5\times V}{288}=\frac{1\times V_2}{298}$

$V_2=1.55V$

i.e. volume of a bubble will be almost 1.6 times to initial volume of a bubble.