Question

An air bubble has a volume of 2.0 cm3 when it is released by a submarine 100 m below the surface of a freshwater lake. What is the volume of the bubble (in cm3) when it reaches the surface? Assume that the temperature and the number of air molecules in the bubble remain constant during the ascent. (The density of water is 1,000 kg/m3.)

Answer 1

Answer:

21.35 cm^3

Explanation:

let the volume at the surface of fresh water is V.

The volume at a depth of 100 m is V' = 2 cm^3

temperature remains constant.

density of water, d = 1000 kg/m^3

Pressure at the surface of fresh water is atmospheric pressure,

P = Po = 1.013 x 10^5 N/m^2

The pressure at depth 100 m is P' = Po + hdg

P' = $1.013 \times 10^{5}+ 100 \times 1000 \times 9.8$

P' = 10.813 x 10^5 N/m^2

Use the Boyle's law

P V = P' V'

$1.013 \times 10^{5}\times V = 10.813 \times 10^{5}\times 2$

V = 21.35 cm^3

Thus, the volume of air bubble at the surface of fresh water is 21.35 cm^3.