An air bubble of volume 2.9 cm³ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 °C. The volume of the bubble when it reaches the surface, where the water temperature is 27 °C, is ____ cm³

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Solution

Q.
An air bubble of volume $2.9 c m^{3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 $° C$ . The volume of the bubble when it reaches the surface, where the water temperature is 27 $° C$ , is ____ $c m^{3} .$
(g = 10 $m / s^{2}$ , density of water = $10^{3} k g / m^{3}$ , and 1 atm pressure is $10^{5}$ Pa) [2026]

1 2.0

2 4.2

3 3.0

4 4.5

Ans.
(4)

$For an air bubble rising in water, the number of moles remain constant$

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$\frac{(P_{atm} + ρ g h) 2.9 {cm}^{3}}{290 K} = \frac{(P_{atm}) V_{2}}{300}$

$V_{2} = 4.5 {cm}^{3}$

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