Question

A diver under water uses breathing apparatus at a depth where the pressure is 1.25 × 10^5 Pa. A bubble of gas breathed out by the diver has a volume of 20cm^3 when it is released. The bubble moves upwards to the surface of the water. At the surface of the water, the atmospheric pressure is 1.00 × 10^5 Pa. The temperature of the water is the same at all depths. What is the volume of this bubble when it reaches the surface?

Answer 1

25 cm³ is the required answer.

GIVEN:

• Pressure under the water , p = 1.25 × 10⁵ Pascal.

• Volume of bubble under water , v = 20 cm³

• Pressure at the surface of water , P = 1 × 10⁵ Pascal.

TO FIND:

Volume of bubble at the surface, V

FORMULA:

According to ideal gas equation, PV = nRT

Here n is the number of moles.

R is the gas constant.

T is the temperature.

From the question , it is clear that temperature at all depth of water is same. So the temperature is constant.

n, R and T are constant. The only variables are pressure and volume.

PV = constant.

BOYLE'S LAW:

Boyle's law states that at constant number of moles and at constant temperature, pressure is inversely proportional to volume of the gas.

According to Boyle's law,

Pressure is inversely proportional to volume.

pv = constant

pv = PV

SOLUTION:

$pv = PV \\ \\ 1.25 \times {10}^{5} \times 20 = 1 \times {10}^{5} \times V \\ \\ V = \frac{1.25 \times {10}^{5} \times 20}{1 \times {10}^{5} } \\ \\ V = 1.25 \times 20 \times \frac{ {10}^{5} }{ {10}^{5} } \\ \\ V = 1.25 \times 20 \\ \\ V = 25 \: {cm}^{3}$

ANSWER:

Volume of bubble at the surface is 25 cm³.