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

Question

A bubble of air is underwater at temperature 15°C and the pressure 1.5 bar. If the bubble rises to the surface where the temperature is 25°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

Tardigrade Admin · Accepted Answer

∵ (p1 V1/T1)=(p2 V2/T2) (By ideal gas equation) or (1.5 × V1/288)=(1 × V2/298) V2=1.55 V1 i.e., volume of bubble will be almost 1.6 times to initial volume of bubble.

Q. A bubble of air is underwater at temperature $1 5^{\circ} C$ and the pressure $1.5$ bar. If the bubble rises to the surface where the temperature is $2 5^{\circ} C$ and the pressure is $1.0$ bar, what will happen to the volume of the bubble ?

Volume will become greater by a factor of 1.6

Volume will become greater by a factor of 1.1

Volume will become smaller by a factor of 0.70

Volume will become greater by a factor of 2.9

$∵ \frac{p _{1} V _{1}}{T _{1}} = \frac{p _{2} V _{2}}{T _{2}}$ (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.

Q. A bubble of air is underwater at temperature 15∘C and the pressure 1.5 bar. If the bubble rises to the surface where the temperature is 25∘C and the pressure is1.0 bar, what will happen to the volume of the bubble ?