Question

A bubble of air is underwater at temperature $15^{0}C$and pressure $1.5$bar. If the bubble rises to the surface where the temperature is $25^{0}C$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

Answer: (A)

Volume will become greater by a factor of $1.6$

Answer 2

: We know that from ideal equation,

$V \propto \frac{T}{P}$

Given $T_{1} = 15 + 273 = 288k,P_{1} = 1.5bar$

$T_{2} = 25 + 273 = 298k,P_{2} = 1bar$

$V_{1} \propto \frac{288}{1.5}`$i.e., $V_{1} \propto 192;V_{2} \propto \frac{298}{1}$

$\frac{V_{2}}{V_{1}} = \frac{298}{192} = 1.55 \approx 1.6$