# A bubble of air is underwater at temperature $15^{o}C$ and the pressure 1.5bar. 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? Option 1) Volume will become greater by a factor of 1.6 Option 2) Volume will become greater by a factor of 1.1 Option 3) Volume will become smaller by a factor of 0.70 Option 4) Volume will become greater by a factor of 2.5

D Divya Saini

Ideal Gas Law -

$PV=nRT$

- wherein

P - Pressure

V - Volume

n - No. of Moles

R - Gas Constant

T - Temperature

We know that from ideal gas equation $V \propto\frac {I}{p}$

given $T_{1} = 273+15$ K= 288K, $P_{1} = 1.5 b\:ar$

$T_{2} = 25 + 273 K$ = 293 K, $P_{2} = 1\: bar$

$V_{1} \propto \frac{288}{1.5}$ $V_{1} \propto 192$

$V_{2} \propto \frac{293}{1}$

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

Option 1)

Volume will become greater by a factor of 1.6

This is correct answer

Option 2)

Volume will become greater by a factor of 1.1

This is incorrect answer

Option 3)

Volume will become smaller by a factor of 0.70

This is incorrect answer

Option 4)

Volume will become greater by a factor of 2.5

This is incorrect answer

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